Hello everyone welcome back to the new video today we will discuss the mensuration chapter okay so basically the mensuration chapter is very important in this we deal with 3D figures about their surface area, about their volume, about their parameters, about the length of the diagonal, about the sides okay so basically we deal with 3D and 3D shapes here in the mensuration chapter okay so in this we will study both the 3D and 3D chapters okay so let's start without any delay let's get started so first of all see in mensuration we study geometry shapes, their area, their volume, their parameters okay and in this we have 2D figures in which we have area and parameters okay in 3D we have volume, curved surface area and total surface area right in 2D figures we deal with all these figures We will do it. Okay, so in rectangle, square, triangle, circle, parallelogram, trapezium, and D figures, we will deal with all these figures like cube, cube, cylinder, cone, sphere, hemisphere. Okay, basically, there are less shortcuts in this chapter. You will have to do calculations in it. You will have to apply the formula and by putting it, your answer will come. Okay, so if you want to speed up your calculation speed in this, you need more practice. Okay, the first figure we have is a rectangle. Okay, in this, we have opposite sides that are equal. We have an angle of 90 degrees. How do we find the area? What is the area? This portion means whatever space is inside the boundary, whatever is the area, how do we find it? Length into breadth. Okay, if we talk about the perimeter, what parameter do we have? Boundary. Okay, the complete boundary, we call it a parameter and it is 2a + pt. We have found the common and the length of Diagonal, okay, this diagonal length, what do we have, we can apply Pythagoras theorem in it, okay, root of l s b square, right, so this is about rectangle, similarly in a square, all sides are equal, all angles are equal, how do we find the area, side into side, okay, suppose I have a side, okay, so what will be the area, a square, side into side, what will be the perimeter, if you add all the sides, right, there are four sides, how much will you get by adding all of them, I have 4a and the length of diagonal, okay, the length of the diagonal, what will we get, is 2a, right, by applying Pythagoras, what is the next figure, triangle, what is the area in it, find out, okay, how will we find the perimeter, how will we find the perimeter, what will we do with all three sides, if we plus them, then you will get the total boundary, okay, what is the area, half the base into height, but some times In the question, we are not given the base height, okay, we are only given the sides, so in that case, what do we apply the Hirose formula to find the area? So, what do we have in the Hirose formula? s s - a s - b s - c is the under root of now, this represents s. This is the semi-parameter. Okay, whatever perimeter you get, how do we find the perimeter? If you divide it by half, then what will we call it? Semi- perimeter. So, if you are given the side of a triangle, then we will find the area using this formula. Let's move ahead. Okay, you can use the same formula. If you want to remember, you can remember it like this for isosceles. Okay, in an equator triangle, all the sides are equal, and we have this formula for the area. Let's move ahead. Regarding the circle, what do we have in the circle? Area. Okay, area means what do we call this entire portion? The value of pi or square pi. What do you mean by this? You will use 22/7 ok circumference what is the circumference of the circle, its perimeter is its boundary, right, so what happens in the case of a circle, 2 pa aa, right, now see, one thing is if you cut the circle from the center like this, what do we get, a semi-circle, okay, if semi, if the area of ​​the entire circle is pa aa sk, then what will be the area of ​​the semi-circle, pa aa sk, if it is halved, okay, but if we talk about the circumference of its perimeter, then see, the circumference of the entire circle, this boundary, what do we have, 2 pi aa, so how much will it be when halved, pi r, okay, but when you halve it, this diameter will also come in the boundary, right, so you will have to add 2 r to it, why 2 aa, because diameter is double of radius, okay, so pa aa will definitely come, half of 2 pa aa, along with that, we have 2 aa, the diameter, that will also be added in the boundary, so what is the circumference of the semi-circle Yes, pa aa p 2, okay, let's move ahead. In a parallelogram, the opposite sides are parallel and equal. Okay, so we calculate the area in it just like we calculate it in a rectangle, length into height. Okay, we always take the height which makes a 90 degree angle with the base and its perimeter is the same as that of a rectangle, 2l p b, right? Because see, if you attach this position from here, okay, then the shape will appear to you like a rectangle, so all the properties will also remain the same. Let's move ahead, let's look at the trapezium. So, what do we have in a trapezium? We have this opposite side, this smaller side and this bigger side, they are parallel to each other, okay, and the difference between them is called the height. Each height is making a 90 degree angle, okay, so in this we try to calculate the area. What is the formula for the area of ​​a trapezium? Half, okay? It is the sum of parallel sides. So, these two sides, a and b, are parallel. There is the same gap between the sum of parallel sides into height. How do we represent the distance between parallel sides? Right from the height, so 1/2 a + b * h. So, we had all these formulas. Okay, you can see this sheet in it. Let's move on to the questions. Question: What is given in this? The area of ​​the square. You are given the area of ​​the square. How much do we find the area of a square? Okay, how much is given? 4096. Okay, what do we have to find in this? Find the ratio of breadth and the length of the rectangle. Whose length is twice the side of the square. Okay, so the length of the rectangle is twice the side of the square. And the breadth is 24 centimeters. And the breadth is 24 cm is less, okay, what do we have to find out, we have to find out the ratio of the breath and the length, so first of all, if we have to find out the length, if we have to find out the breath, first of all we should know a, okay, because both things are depending on a, if we have a s 496 given, then can we find a, we can definitely find it, okay, now you see in this that if you want to estimate a little, what number is the square of a square which is 4096, then you see in this, like if we suppose if we square 60, then we get 3600, okay, and if we square 70, then we get 4900, right, and 4096 is coming in between these two, and it is closer to 3600, that means what will be the value of a, 64, right, because 64, because the square of 4 comes at the end, so the value of a will be 64, so if a The length is 64, its width is 128, okay, so it will come to 128, and the width is 64 - 24 = 40. If you take the ratio of these two, 40 128, then what will be the ratio of these? That is, if you cancel this in the table of eights, it will come to 5, and this will come to us as 16, so option C is the right answer, okay, let's move on to the next question, okay, next question, what do we have? A wire is in the form of a circle of radius 3.5 meters, okay, see what is there in this, like in 2D, if you convert one shape into another shape, its parameters remain the same, okay, that does not change, its total length remains the same, so if you make a circle from a wire and then you convert it into a rectangle, then it means that you first made a circle, after that you made a rectangle, the perimeter of both will remain the same, okay, so The radius of this circle is given to us as 3.5. Okay, if the radius is given, can we find its parameter? It is exactly 2 pi. Okay, you can use the value of pi in this, 22/7, which is 3.5. So if you cancel everything out, what will you get? 22. So, this is the circumference we have, which is the perimeter of the circle. And we will have the same perimeter for this rectangle as well. Okay, how do we find the perimeter of a rectangle? 2l p b. So, 2a p b. How much will I get? 22. So, how much will I get? 11. Okay, look, in this, the ratio of length and breadth is given to you as 6:5. Okay, so we take the length as 6x. We take the breadth as 5x. What is the plus of both? 11. The value of 11x is 11. So, what will I get for x? One. Okay, if x is 1, then what will I get for length? 6x * 6 1 6 will come, how much will the breath come, 5 will come, if the length is six and the breath is 5, then what will be the area? 30, okay, because how do we find the area of ​​a rectangle, length into breath, let's move ahead, next question, what do we have for their areas, okay, that means pa aa2s minus pa aa2s, this is what we have to find, in this the difference of their areas, okay, so first we will find the value of radius r1 r2, okay, if you calculate r1 from here, calculate r2 from here, then you can check, after solving completely from here, r1 which is 42, you will get how much r2 will come, 56, okay, by putting the value of pi in it, 22/7, okay, now see, we have to find the difference of area, pi, you take the common, okay, what will come out to be r2s - r1s, in this you can use the formula of a s - b s, okay, what we have is a - b a + b, so first we will plus both, then add both If you subtract it, you will get 14. If you plus it, you will get 98. Okay, write pi as 22/7. Right, then after multiplying everything, what will be your answer? Option C. So, that is why I am saying that you will have to enhance the speed a little bit in it. Let's move ahead to the next question. Okay, next question, what do you have? What would be the cost of building a 7 meter wide garden around a circular field with diameter 280. Okay, you are given a circular field here whose diameter is 280, that means what will be its radius? 140. Okay, around this, you want to make a 7 meter garden. If you want to make a 7 meter wide garden, then our shape will be like this. You want to make a 7 meter wide garden, so how much will we get from this? 7 meters. Okay, so what do you have to calculate in this, what will be the cost of building a garden? This garden has to be constructed. What will be the cost of doing this, okay and what is given to you for 1 meter square, the cost is ₹21, how much money is being spent for 1 meter square, okay, means first of all we will find out the total area of ​​this garden which is around the circular field and we will multiply it by 21, okay so how can we find out its area, outer area, okay if you subtract the inner area from the outer area, then you will get the area of ​​the garden, okay so for the outer area what is my radius, 147, okay and for the inner area what is my radius, 140, okay so let's apply the formula directly, pa aa2 sk, means pi, you take the common in it, 147 sk, okay minus 140 sk, okay, in this also you can use the formula a s - b s of a - b a p b, okay so when you do all the calculations in this, this sen will come here, here p 287 will come from this, cancel from this, okay, so 22 * ​​287 is your area, you will have to multiply it by 21, right? Why did we do it by 21? Because if ₹ is being charged for 1 meter square, then how much money will be required for this area, we will multiply that by 21 as well. After multiplying this, your option will come, that is C option, okay, let's move ahead to the next question, okay, what is the next question, see the diagram, in this, if you have made a diagram in every question, then you will have better clarity about what is asked, so a cow is tied on the corner of a rectangular field, right? So let's draw a rectangular field once, okay, its dimensions are given to us, 30 20 30, let's take its length, 20, let's take its breadths, okay, the cow is tied on the corner, so let's take this corner, suppose by a 14 meter drop, okay, by a 14 meter drop. The cow is tied here, so how much area can it graze? Okay, now see, this point will be the central point. This is the rope, so how much area can the cow graze? Okay, it will graze in a circle because we will have the center and radius. But which one do we have to take inside the rectangle field, because that is the field, it will graze from that only. Right, how much will this come? It is a quarter, it is an angle of 90 degrees. Okay, this will be a quarter of the circle, that is, what did we find out? Why did we do it with 4 four because it is a quarter of the circle. Okay, just use this and you know the radius is 14. Okay, put the value of 14 and divide it and you can see the answer in it, how much is it coming out? It was not used here, we just found the answer from the radius. Okay, let's move ahead. Okay, this is also of the same type, there is a little difference in it at each corner of the triangular field, the side of the triangular field. The side given to us in this is 26, 28 and 30. We have rope on each corner of this. In this also, the length of rope is 7 meters. So this cen will come, this cen will come, this cen will come, so how much area can it graze here? This is this much here and this here. Okay, the area ungrazed by the cow, how much area will it not graze? Okay, we have to find that, that is, we have to find this portion, this area. Okay, how can we find this area? First, we will find the area of ​​the entire ray triangle. Okay, the triangle area is the area of ​​these three which are being formed here, so how will we find out how much area these three are coming out to be? We know that the sum of the three angles in a triangle is 180. We do not know this angle. We do not know this angle. But we do know that the total of all three will be 180. That means if we combine all three, we will find the radius. Their sum is the same. If we combine all three, we will have a semi-circle of 180 degrees. So, we can find its area. Exactly pa aa sba 2 is half of the entire circle. So pa aa sba 2 is half. So, first of all, you can find the area of ​​the triangle in this. Now see, whenever you are given the sides, how can we find the area of ​​the triangle? By using the Hirose formula. So, you can use the Hirose formula in this. s s - a s - b s - c. Okay, and pa aa sba 2, what will you do with this? You can easily find the value of s. What is the semi-perimeter? What will be the perimeter in this? 26 p 30 p 28. If you do this, then how much will you get? 54 54 p 30 84. Okay, you have to halve 84. Okay, you will get the value of 42 42s. What is the value of a? 26 What is the value of b? 28 What is the value of c? 30 Okay, what is the value of aa? Okay, after putting all the values, tell me the answer once, how much is coming, which option is coming for you, let's move ahead to the next question. Next question, what do you have? The radius of a circular field is equal to the side of a square field, right? The radius of the circular field is equal to the side of the square field, right? That means, this side is also r. Then, both the radius and the side are equal. If the difference between the perimeter of the circle and the square is 32, the gap between this and its perimeter is 32, right? So, what is the perimeter of the circle? 2 pa. Okay, we have the perimeter of the square four times the side, this is given as 32. Okay, so we have to find the parameter of the square in this, that means we have to find the value of 4r. First of all, we will find the value of r from this equation. Okay, take r as common in this, here it is pi. Put the value 22/7 in this, okay, so when you solve it completely, it will come out to be 44/1, okay, then it will come out to be 16/7, right, from here, what will be the value of r that you have? 14, okay, if r is 14, then what will be the four times of 14, 56, okay, let's move ahead to the next question, okay, what is there in this, we have a circular paper sheet whose circumference is given as 352, okay, and we have to cut two circular plates of maximum size from this, okay, see, from this circular sheet, if we have to cut two circular plates of maximum size, then of course their radius will be half of this, right, what will we get with the first circular sheet, this one is okay, and the second one will come, it has to be cut in the form of a circle, so we can cut only this much maximum, okay, now see, the radius of these two circular sheets that you have cut will be half of this complete one, okay, if the radius of the complete is Here it is this much, so this much will be half of it, right here if the radius is halved then its circumference will also be halved, okay so directly you will halve 352, how much will the half of 352 be, 176 option A will come correct in this, okay let's move ahead to the next question, okay this is also the same type of question in which I told you that when one D shape changes into another, its parameters remain the same, so in this your first wire which was in square form, then you bent it into circle form, okay earlier the wire which was in square form, you changed it into circle form, okay when it was in square form, its area was 121, you have been told that when it is changed into a circle, then what will be its area, okay so we know that if we take its side a, okay so how much a is given, 121 means how much a will I get, 11, right so the parameters of both of these will remain the same, okay perimeter if side 11 So the perimeter will be 44. Okay, this means how much perimeter of the circle will I have? 44. Okay, this means how much will I have? 22. How much will I have? 7. Okay, if r is from me, then can we tell how much area will I have? 22. 7. So, if r is from me, then can we tell how much will I have? 154. So option C is the right answer. Okay, so the area of ​​the circular circle is more than the square. It will be enclosed here. Okay, next question. Okay, next question. We have four circles having equal radius. Okay, right? Okay, at the four corners of the circle, there are four circles of equal radius. Okay, and they are touching each other. Okay, big and small, all are equal. Okay, in this we have the remaining area of ​​8. How much is the remaining area given to us? 168 cm square. We have to tell what is the size of the radius. We have to tell the radius. The radius of all the circles is the same. Okay, so can we find this out? Of course we can find it. You will make an equation in it. Okay, first of all see that if we have radius AA, then what will be the side? I will have 2AA, which is the side of the square. Okay, now how can we find this remaining area? If we subtract these four positions from the area of ​​the entire square, then I will get this remaining value. What is the area of ​​the entire square? What is the side square side? 2AA, 2AA square, what will be 4AA square? What have I subtracted from 4AA square? These are four quadrants. So see, these four quadrants, what will these four together make? A complete circle. Okay, what is a circle? AA square, what is the minus of these? 168. Okay, this You can find the value of r by solving the equation, okay, so your value of r will come easily from this, tell me which option is coming for you, the value of r in it, after solving it, okay, let's move ahead to the next question, okay, next question, what is the area of ​​the triangle, this is the ratio of the sides of the triangle, okay, the perimeter of the triangle, we have to find the perimeter of the triangle, see these triplets, these are the Pythagorean triplets, 3 4 5, okay, what are triplets, in which, like the square of 3 is 9, the square of 4 is 16 and the square of 5 is coming out equal to the sum of these two, Pythagoras theorem c s = a s + b s, right, this means that this triangle is not normal, we have a right angle triangle, so how do we find the area of ​​a right angle triangle, t is half base into height, so area in give No it is 216 Okay so if we draw this triangle we take the base in it 3x Okay let's take the height 4x what will be the hypotenuse 5x Okay 3x what is the height 4x Okay if you cancel Okay after cancelling you will get the final result here 36 x s 36 means what will be the value of x 6 Okay we have to find the perimeter what is perimeter is the sum of all the sides 4x 3x 5x if we combine all then it becomes 12x if the value of x is 6 then 12 * 6 will be what we will get 72 so we will get the parameter of option D Okay let's move ahead Okay so these were the questions of D we discussed 11 questions in it Okay rest if you have any doubt in any question or any different question then you can ask Okay so thank you all