Bidyut Guha Thakurta and Amitava Mitra Solutions for Exercise 1: EXERCISE 4

If the ratio of volumes of two right circular cones is $16:27$ and the ratio of their radii is $2:3$, then the ratio of their heights is

If the height and slant height of the right circular cone is $15 \mathrm{cm} \mathrm{and} 17 \mathrm{cm}$, then the diameter of the base is

If the area of the base of a right circular cone is $154 \mathrm{sq}.\mathrm{cm}$ and the volume is $308 \mathrm{cc}$, then its height is

If the volume of the right circular cone is $352 \mathrm{cc}$ and height is $21 \mathrm{cm}$, then the diameter of the base is 

If the area of curved surface area of right circular cone is $\sqrt{5}$ times the area of the base, then the ratio of its height and radius is

Keeping the radius of a cone fixed, if the height is doubled, then the volume of the cone is increased by

If the area of curved surface area of right circular cone is twice the area of the base, then the ratio of its height and diameter is

If the height and radius of base of the cone are $h$ and $r$, then its volume is $\frac{1}{3}\mathrm{\pi }r\times$  _____.