Question

The surface area of a solid metallic sphere is $616c{m}^2$. It is melted and recast into a smaller sphere of diameter 3.5 cm. How many can such spheres be obtained?

• A. 32
• B. 64
• C. 48
• D. 96

Answer 1

The correct option is B

64

Let R be the radius of the solid metallic sphere.
Then, its surface area is given by,
$4\pi R^2=616c{m}^2$ [Given]
$\Rightarrow 4\times \frac{22}{7}\times R^2=616$
$\Rightarrow R^2=\frac{616\times 7}{4\times 22}=49\Rightarrow R=\sqrt{49}$
= 7 cm.
$\therefore$ Number of small spheres formed
$=\frac{Totalvolumeofsolidmetallicsphere}{Volumeofasmallmetallicsphere}$
$=\frac{\frac{4}{3}\pi (7{)}^3}{\frac{4}{3}\pi {\left(\frac{3.5}{2}\right)}^3}=64$
Hence, 64 small spheres can be obtained.