Question

A hollow sphere of the internal and external radius of 6 cm and 8 cm respectively is melted and recast into small cones of base radius 2 cm and height 8 cm. Find the number of cones.

Answer 1

Volume of material in hollow sphere $=\frac{4}{3}\pi (R^3-r^3)$ { Where $R=8cm,r=6cm$}

Number of cones $=\frac{volumeofhollowsphere}{volumeofonecone}$ {Where radius of cone $r_1$ $=2cm$ and height of cone $h=8cm$}

$=\frac{\frac{4}{3}\pi (R^3-r^3)}{\frac{1}{3}\pi \left(r^{2}h\right)}$

$=\frac{4(R^3-r^3)}{r^{2}h}$

$=\frac{4(8^3-6^3)}{2^2\times 8}$

$=37$ Cones