Question

Find the slant height and vertical height of a cone with radius $5.6\text{cm}$ and curved surface area $158.4$ cm${}^2$

• A. $9\text{cm}$ and $8.07\text{cm}$
• B. $9\text{cm}$ and $7.05\text{cm}$
• C. $8\text{cm}$ and $8.07\text{cm}$
• D. None of the above

Answer 1

The correct option is B $9\text{cm}$ and $7.05\text{cm}$

Given, Radius $=5.6\text{cm}$

and curved surface area $=158.4{\text{cm}}^2$

Let vertical height $=h$, slant height $=$ $l$

Then,
Curved surface area of cone $=\pi rl$
$\Rightarrow \frac{22}{7}\times 5.6\times l=158.4$
$\Rightarrow l=\frac{158.4\times 7}{22\times 5.6}=\frac{18}{2}=9\text{cm}$

We know, $l^2=r^2+h^2$.
Thus $h^2=l^2-r^2$

$=9^2-(5.6{)}^2$
$=81-31.36$
$=49.64$.
Therefore, $h=\sqrt{49.64}$
$⟹$ $h=7.05\text{cm}$ (approx.)

Hence, option $\text{B}$ is correct.