Question

A sphere is formed by melting $96$ cones of radius $1.5cm$ and height $4cm$. Find the radius of the sphere.

Answer 1

volume of 1 cone = $\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi \times {1.5}^2\times 4=3\pi c{m}^3$

= $\frac{22}{7}\times 3=\frac{66}{7}$

volume of 96 cones =$96\times 3\pi =288\pi c{m}^3$

now, this volume = volume of sphere..

$\frac{4}{3}\pi r_1^3=288\pi$

$r_1^3=\frac{288\times 3}{4}=72\times 3=2^3\times 3^3=6^3$

$r_1=6cm$