Question

The radius and height of a cone are in the ratio $4:3$. The area of the base is $616$ $c{m}^2$. The area of the curved surface (in $c{m}^2$) of the cone is _____. (Given π = $\frac{22}{7}$)

• A. 870
• B. 970
• C. 770
• D. 670

Answer 1

The correct option is C 770

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

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

$\Rightarrow \pi$$r^2=616$

$\Rightarrow \frac{22}{7}$×$r^2=616$

$\Rightarrow r^2=196$

$\Rightarrow r=14cm$

So,
$h=\frac{3}{4}\times 14=\frac{21}{2}=10.5cm$

$\Rightarrow l=\sqrt{h^2+r^2}$

$\Rightarrow l=\sqrt{{10.5}^2+{14}^2}$

$\Rightarrow l=\frac{35}{2}=17.5cm$

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

$=\frac{22}{7}\times 14\times \frac{35}{2}$

$=770c{m}^2$