Question

A closed cone tank radius $7$ cm and height $10$ cm is made from a sheet of aluminium. How much sheet is required?

• A. $144c{m}^2$
• B. $22\sqrt{149}c{m}^2$
• C. $(22\sqrt{149}+154)c{m}^2$
• D. None of the above

Answer 1

The correct option is C $(22\sqrt{149}+154)c{m}^2$

Given, radius of the cone $r=7cm$ and height $h=10cm$.

Then, slant height $s=\sqrt{h^2+r^2}$

$s=\sqrt{7^2+{10}^2}$

$=\sqrt{49+100}$ $=\sqrt{149}$.

We know, total surface area of cone = Area of base + Area of curved surface
$=\pi r^2+\pi rs$.

$=\frac{22}{7}\times 7\times 7+\frac{22}{7}\times 7\left(\sqrt{149}\right)$

$=154+22\sqrt{149}c{m}^2$.

Therefore, option $C$ is correct.