Question

If the curved surface area of a right circular cone is $12,320c{m}^2$ and its base radius is $56$ cm, then its height is $(\pi =\frac{22}{7})$:

• A. $42$ cm
• B. $36$ cm
• C. $48$ cm
• D. $50$ cm

Answer 1

The correct option is A $42$ cm

We know, curved surface area of a cone $=\pi rl$, where $r$ is the radius of the cone and $l$ is the slant height.
Hence, curved surface area of this cone, $=\frac{22}{7}\times 56\times l=12320c{m}^2$

$\therefore l=70cm$.

For a cone, $l=\sqrt{h^2+r^2}$, where $h$ is the height.

Hence, $70=\sqrt{h^2+{56}^2}$

$\Rightarrow 4900=h^2+3136$

$\Rightarrow h^2=1764$

$\Rightarrow h=42$ cm .

Therefore, option $A$ is correct.