Answer to Question #315270 in Geometry for rei

Question

A conical vessel has a height of 24 cm and a base diameter of 12cm. It holds water to a depth of 18 cm above its vertex. Find the volume in cubic cm of its content.

Answer 1

Height of cone = 24cm

Base diameter= 12cm

Depth of water = 18cm

Diameter at the level of water = x cm

Using ratio and proportion:

(12/24) = (x/18)

x = (18*12)/24

x= 9cm

Radius at the level of water = 9/2 = 4.5cm

Volume = (1/3) * (22/7) * r² * h

= (1/3)*(22/7)* 4.5² * 18

= 381.9cm³