Question

A metallic sphere of radius 10.5 cm is melted and thus recast into small cones each of radius 3.5 cm and height 3 cm. Find how many cones are obtained.

Answer 1

Radius of a metallic sphere $\left(R\right)=10.5cm\therefore Volume=\frac{4}{3}\pi R^3=\frac{4}{3}\pi (10.5{)}^{3}c{m}^3=\frac{4}{3}\times \pi \times 1157.625c{m}^3$
Now radius of a small cone = 3.5 cm and height = 3 cm
$\therefore$ Volume of one cone $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi (3.5{)}^2\times 3$$c{m}^2$
$=\frac{1}{3}\pi 12.5\times 3$$c{m}^3$
$=12.25\pi c{m}^3$
Now number of cones made from the volume of sphere $=\frac{4\times 1157.625\pi }{3\times 12.25\pi }=126cones$