Question

A metallic sphere of radius 10.5 cm is melted and then recast into small cones each of radius 3.5 cm and height 3 cm. Find how many cones are obtained? [4 MARKS]

Answer 1

Formula: 1 Mark
Application: 1 Mark
Solution: 2 Marks

Volume of the sphere $=\frac{4}{3}{R}^3$
$=\frac{4}{3}\pi \times (10.5{)}^{3}c{m}^3$
Volume of a cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi (3.5{)}^2\times 3c{m}^3$
$\therefore$No. of cones recast
$=\frac{Volumeofthesphere}{Volumeofacone}$
$=\frac{\frac{4}{3}\pi \times 10.5\times 10.5\times 10.5}{\frac{1}{3}\pi \times 3.5\times 3.5\times 3}=126cones$