Question

The radius and height of a cone are in the ratio 4: 3. The area of the base is 154 cm². The curved surface area of the cone is :

• A. 192.5 cm²
• B. 152 cm²
• C. 184.5 cm²
• D. 162.5 cm²

Answer 1

The correct option is A 192.5 cm²

Given,
$\frac{r}{h}$ = $\frac{4}{3}$

Base area = $\pi$$r^2=154$
$\Rightarrow \frac{22}{7}\times r^2=154$

$\Rightarrow r^2=\frac{154\times 7}{22}$

$\Rightarrow r=7cm$

$\Rightarrow h=\frac{3}{4}\times 7=\frac{21}{4}cm$

$\Rightarrow l=\sqrt{(h^2+r^2)}$
$\Rightarrow l=\sqrt{{\left(\frac{21}{4}\right)}^2+7^2}$
$=\frac{35}{4}cm$

The curved surface area = $\pi$$rl$

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