Question

the diameter of the bottom of a frustum of right circular cone is 10cm and that of the top is 4cm and height is 4cm find out the area of The total surface and the volume of frustum

Answer 1

I hope that this will help you.

Answer 2

The volume of the frustum of cone is 653.451 cm³ and total surface area of the frustum of cone is  681.586 cm².

• The radius of the top of the frustum of cone is given as 4 cm and the bottom the cone is 10 cm, height of the cone is given as 4 cm.
• Now, we have to calculate the total surface area of the frustum of cone and the volume of the cone.
• We calculate the volume of cone first by using the formula,

V = $\frac{1}{3}*\pi * h * (r_1^2 + r_2^2 + r_1*r_2)$ ,

where $r_1$ and $r_2$ are the radius of the top and bottom of the frustum and h is the height of the cone.

• Now substituting the values in the above formula, we get

V = $\frac{1}{3}*\pi * 4 * (10^2 + 4^2 + 4*10)$  = 653.451 cm³.

• Now the total surface area of the frustum of cone is

TSA = $π * [ r_1^2 + r_2^2 + (r_1 + r_2) * \sqrt{((r_1 - r_2)^2 + h^2)} ]$

• Now substituting the values in the above formula, we get

TSA = $π * [ 10^2 + 4^2 + (10 + 4) * \sqrt{((10 - 4)^2 + 4^2)} ]$ = 681.586 cm².