Question

A solid toy is in the form of a hemisphere surmounted by a right circular come. Height of the cone is 2 cm and the diameter of the base is 4 cm. If a right circular cylinder circumscribes the toy, find how much more space it will cover.

Answer 1

Given radius of cone, cylinder & hemisphere (r) = \(\frac{4}2\) = 2 cm

 Height of cone (l) = 2 cm 

Height of cylinder (h) = 4 cm 

Volume of cylinder = πr² h =π(2)² (4) cm …….. (1) 

Volume of cone = \(\frac{1}3\)πr²l

= \(\frac{1}3\) π(2)² x 2

= \(\frac{2}3\) x 4 x 2 cm.........(3)

So remaining volume of cylinder when toy is instead to it

= 16π – 8π 

= 8π cm³ 

∴ So remaining volume of cylinder when toy is instead to it = 8π cm³