29 one â ‹Q29 In Fig 10, a right circular cone of diameter r cm and height - Maths - Surface Areas and Volumes

Question

29 one

â€‹Q29 In Fig 10, a right circular cone of
diameter r cm and height 12 cm rests on the base of a right
circular cylinder of radius r cm Their bases are in the same plane
and the cylinder is filled with water upto a height of 12 cm If the
cone is then removed, find the height to which water level will
fall

Lalit Mehra · Accepted Answer

Let the radius of base of cylinder and cone be r cm.

Height of water in the cylinder = Height of the cone, h = 12 cm.

Volume of water

$= π r^{2} (12 cm) - \frac{1}{3} π r^{2} \times 12 cm = π r^{2} (12 - 4) {cm}^{3} = 8 π r^{2} {cm}^{3}$

Let the height of water in the cylinder be h' an when the cone is removed.

Volume of water = 8πr²cm³

∴ πr²h' = 8πr²

⇒ h' = 8

Thus, the level of water in the cylinder is 8 cm.

-2