Question

If cuboid of size $(8\times 4\times 2)c{m}^3$ is melted and reshaped as cylinder of height $7$ cm, find the radius of cylinder.

• A. $\frac{16}{\sqrt{22}}$cm
• B. $\frac{8}{\sqrt{22}}$cm
• C. $\frac{4}{\sqrt{22}}$cm
• D. None of the above

Answer 1

The correct option is B $\frac{8}{\sqrt{22}}$cm

Since, the cuboid is melted to form a cylinder,

$\text{Volume of cuboid}=\text{Volume of cylinder}$

Volume of cuboid $=l\times b\times h$

$=8\times 4\times 2=64c{m}^3$

$\therefore$ Volume of cylinder $=64c{m}^3$

Now, Volume of cylinder $=\pi r^{2}h$

$64=\pi r^2\times 7$

$\therefore r^2=\frac{64}{7}\times \frac{7}{22}$

$\therefore r=\sqrt{\frac{64}{22}}=\frac{8}{\sqrt{22}}$ cm