Question

Choose the correct answer from the alternatives given.
By melting a solid lead sphere of diameter $12$ cm, three a small spheres are made whose diameters are in the ratio $3:4:5$.
The radius (in cm) of the smallest sphere is

• A. $3$
• B. $6$
• C. $1.5$
• D. $4$

Answer 1

Answer: (A)

$3$

We know that

Volume of sphere $=4/3\pi r^3$

Given $D=12cm$

$\therefore r=6cm$

Volume of big sphere $=\frac{4}{3}\times x\times 216$

$=288x$

According to Question

$288x=\frac{4}{3}x(27x^3+64x^3+125x^3)$

$\frac{288\times 3}{4}=216x^3$

$x=1cm$

$\therefore$ Radius of smallest sphere $=3cm$