The volume of a right circular cone is equal to the volume of that right circular cylinder whose height is 27 cm and diameter of its base is 30 cm. If the height of the cone is 25 cm, then what will be the diameter of its base?

Given, Height of the cylinder = 27 cm
Radius of the cylinder = 30/2 = 15 cm
Volume of the cylinder = $$\pi \times 15^2 \times 27$$
Given, Height of the cone = 25 cm
Let radius of the cone be r cm
Volume of the cone = $$\dfrac{1}{3} \times \pi \times r^2 \times 25$$
Given, Volumes of the cone and cylinder are equal.
$$\pi \times 15^2 \times 27 = \dfrac{1}{3} \times \pi \times r^2 \times 25$$

=> $$r^2 = \dfrac{15^2 \times 9^2}{5^2}$$

=> $$r = \dfrac{15\times9}{5} = 27$$

Radius of the base of the cone = 27 cm
Then, Diameter of the base of the cone = 54 cm.