Question

The maximum possible sphere is carved out of a cube of edge $7\mathrm{cm}$. Find its surface area (in ${\mathrm{cm}}^2$ ).

• A. 154
• B. 231
• C. 308
• D. 616

Answer 1

Answer: (A)

Diameter of the sphere $=$ the edge of the
$\text{ cube }=7\mathrm{cm}$
$\Rightarrow 2r=7\mathrm{cm}\Rightarrow r=\frac{7}{2}\mathrm{cm}$
$\therefore \text{ Surface area }=4\pi r^2=4\times \frac{22}{7}\times {\left(\frac{7}{2}\right)}^2$
$=154{\mathrm{cm}}^2$