Question

find the volume of frustum of cone areas of whose ends are 40 square metre and 10 square metre and height is 9 metre​

Answer 1

Answer:

The Volume of the frustum is 213.6456 cubic meter.

Step-by-step explanation:

Given : Frustum of cone areas of whose ends are 40 square meter and 10 square meter and height is 9 meter.

To find : The volume of the frustum ?

Solution :

The area of the one end of cone is $A_1=40\ m^2$

The radius of the one end of frustum is $A=\pi {r_1}^2$

$40=\pi {r_1}^2$

$r_1=\sqrt{\frac{40}{\pi}}$

$r_1=3.56\approx 3.6$

The area of the other end of cone is $A_2=10\ m^2$

The radius of the other end of frustum is $A=\pi {r_2}^2$

$10=\pi {r_2}^2$

$r_2=\sqrt{\frac{10}{\pi}}$

$r_2=1.78\approx 1.8$

The height is h=9 meter.

The volume of the frustum is

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

Substitute the value,

$V = \frac{1}{3}\times 3.14\times 9((3.6)^2 +(1.8)^2+ (3.6\times1.8))$

$V = \frac{1}{3}\times 3.14\times 9(12.96 +3.24+6.48)$

$V = \frac{1}{3}\times 3.14\times 9\times 22.68$

$V = 213.6456\ m^3$

Therefore, The Volume of the frustum is 213.6456 cubic meter.