A solid toy is in the form of a hemisphere surmounted by a right circular cone.The height of the cone is 4 cm and diameter of the base is 8 cm.Determine the volume of the toy.If a cube circumstances the toy,then find the difference of the volumes of cube and the toy.Also,find the total surface area of the toy.

volume of toy = volume of cone + volume of hemisphere

$\frac{1}{3}\times \pi r^2\times h+\frac{2}{3}\times \pi \times r^3=\frac{1}{3}\times \pi \times r^2(h+2r)=\frac{1}{3}times\pi \times 4^2\times 12=64\pi =200.96c{m}^3$



if the cube circumscribes the toy ,
then its side = height of toy = diameter of toy = 8cm
volume of cube = $8^3=512c{m}^3$

difference in volume of cube and toy
= 512 - 200.96
= 311.04 $c{m}^3$