Question

The total surface area of a cone is $770c{m}^2$. If its slant height is four times the radius of the cone, the diameter of the cone is:

• A. $14cm$
• B. $7cm$
• C. $20cm$
• D. $18cm$

Answer 1

The correct option is A $14cm$

Given, the total surface area of cone $TS{A}_{cone}=770c{m}^2$.
Also, $l=4r$.

$\therefore TS{A}_{cone}=\pi rl+\pi r^2=\pi r\times \left(4r\right)+\pi r^2$
$⟹$ $770=5\pi r^2$
$⟹$ $r^2=\frac{770}{5\times 22}\times 7=49$

$\therefore r=\sqrt{49}=7$.

$\therefore$ Diameter, $d=2\times 7=14cm$.

Hence, option $A$ is correct.