Question

The height and the radius of the base of a right circular cone is half the corresponding height and radius of another bigger cone.Find:(i)the ratio of their volumes. (ii)the ratio of their lateral surface areas.

Answer 1

answer is here...............

Answer 2

The ratio of their volumes is 1:8 and the ratio of their lateral surfaces is 1:4.

• Let us assume the height and radius of the bigger right circular cone be 2r and 2h respectively.

Now the radius and height of the smaller right circular cone will be r and h respectively.

• Volume of the right circular cone is given as 1/3πr²h.

Now ratio of volume of smaller cone to the bigger cone = $\frac{\frac{1}{3}\pi r^2h}{\frac{1}{3} \pi (2r)^2 (2h)}$

Ratio of volume of smaller cone to the bigger cone = 1/8

Ratio of volumes is 1:8

• Lateral surface area of cone = πr√(r²+h²)

Now ratio of lateral surfaces of smaller cone to the bigger cone = $\frac{\pi r \sqrt{r^2 + h^2}}{\pi (2r) \sqrt{(2r)^2 + (2h)^2}}$

Ratio of lateral surfaces of smaller cone to the bigger cone = 1/4

Ratio of lateral surfaces is 1:4