Question

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

Answer 1

Solution:

Given that,

Radius of the cone, cylinder and hemisphere (r) = 2 cm

Height of the cone (l) = 2 cm

Height of the cylinder (h) = 4 cm

Volume of the cylinder ,$V_1=\pi r^{2}h=\pi \times 2^2\times 4=16\pi c{m}^3$……… (1)

Volume of the cone ,$V_2=\frac{1}{3}\pi r^{2}L=\frac{1}{3}\pi \times 2^2\times 2=\frac{8}{3}\pi c{m}^3$ ………. (2)

Volume of the hemisphere ,$V_3=\frac{2}{3}\pi \times 2^3=\frac{16\pi }{3}c{m}^3$ ………. (3)

So, remaining volume of the cylinder when the toy is inserted to it = V₁ – (V₂ + V₃)

V = 16π – 8 π = 8 π cm³

Hence, remaining volume of the cylinder when toy is inserted into it = V = 8π cm³