Question

A solid metal cone with radius of base $12$ cm and height $24$ cm, is melted to form spherical solid balls of diameter $6$ cm each. Find the number of balls thus formed.

• A. $30$
• B. $31$
• C. $32$
• D. $34$

Answer 1

The correct option is C $32$

Volume of cone$=\frac{1}{3}\pi r^{2}h$

Here, for cone $r=12,h=24$

$=\frac{1}{3}\times \pi \times {12}^2\times 24=\frac{1}{3}\times \pi \times 144\times 24$

$=1152\pi c{m}^2$

Volume of balls(sphere) $=\frac{4}{3}\pi r^3$

Here, for ball $r=\frac{6}{2}=3$

$\frac{4}{3}\pi \times 3^3=36\pi$

No. of balls$=\frac{1152\pi }{36\pi }=32$

Thus 32 balls will be formed.