Question

(a) A solid sphere of radius 15 cm is melted and recast into solid right circular cones of radius 2.5 cm and height 8 cm. Calculate the number of cones recast.

(b) A hollow sphere of internal and external radii 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. [6 MARKS]

Answer 1

Each Part: 3 Marks

(a) Number of cones recast
$=\frac{Volumeofthesphere}{Volumeofacone}=\frac{\frac{4}{3}\pi \times {15}^3}{\frac{1}{3}\pi \times 2.5\times 2.5\times 8}$

$=\frac{4\times 3375}{6.25\times 8}=\frac{13500}{50}=270cones$


(b) Volume of hollow sphere
= No. of cones $\times$ volume of a cone
$\therefore$ No. of cones $=\frac{\frac{4}{3}\pi (8^3-6^3)}{\frac{1}{3}\pi \times 2^2\times 8}$
$=\frac{4(512-216)}{32}=37$