Question

The radius and height of a cone are in the ratio 4: 3. The area of the base is 154 cm². The area of the curved surface in $c{m}^2$ is

• A. 192.5
• B. 190.5
• C. 182.5
• D. 162.5

Answer 1

The correct option is A

192.5

Let the radius and height of the cone be $r$ and $h$

Base area $=\pi r^2=154$

$\Rightarrow r=7cm$

$\therefore h=\frac{3}{4}\times 7=\frac{21}{4}cm$ (Given that $\frac{r}{h}=\frac{4}{3}$)

From the relation $l^2=h^2+r^2$
$\Rightarrow l=\sqrt{(h^2+r^2)}$

$=\sqrt{({\left(\frac{21}{4}\right)}^2+7^2)}$

$=\sqrt{\frac{441+49\times 16}{16}}$

$=\sqrt{\frac{1225}{16}}$

$\therefore l=\frac{35}{4}cm$

$\Rightarrow$ So, curved surface area = $\pi rl$

$\Rightarrow$ $\frac{22}{7}\times \left(7\right)\times \frac{35}{4}=192.5c{m}^2$