Question

A conical container can hold 120π cubic centimeters of water. The diameter of the base of the container is 12 centimeters. The height of the container is centimeters. If its diameter and height were both doubled, the container's capacity would be times its original capacity.

Answer 1

Im pretty sure the height of the container is 10 centimeters. If its diameter and height were both doubled, the container's capacity would be 8 times its original capacity.

Answer 2

Answer :

Volume of conical container = 120π cm³

Diameter of the base of the container = 12 cm

So, Radius = 6 cm

$\text{Volume of cone = }\frac{1}{3}\pi\times radius^2\times height\\\\\implies 120\pi=\frac{1}{3}\pi\times 6^2\times height\\\\\implies height = \frac{120\times 3}{36}\\\\\implies height = 10\text{ cm}$

Hence, height = 10 cm

Height is doubled = 20 cm

Diameter is doubled = 24 cm

So, radius = 12 cm

$Volume=\frac{1}{3}\pi\times radius^2\times height\\\\\implies Volume = \frac{1}{3}\pi\times 12^2\times 20\\\\\implies Volume = 24\times 120\pi$

Hence, The new volume become 24 times of the previous one.