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 of cone is ___

• A. $192.5{\text{cm}}^2$
• B. $212.5{\text{cm}}^2$
• C. $100.5{\text{cm}}^2$
• D. $102.5{\text{cm}}^2$

Answer 1

The correct option is A $192.5{\text{cm}}^2$

Given, Solid:Cone
Height of cone $=h$
Radius of base $=r$
$\frac{r}{h}=\frac{4}{3}$

Base area, $\pi r^2=154$
$\Rightarrow r=7\text{cm}$

So,
$h=\frac{3}{4}\times 7=\frac{21}{4}$

Length of cone, $l=\sqrt{(h^2+r^2)}=\frac{35}{4}$

So, curved surface area of cone $=\pi rl=\frac{22}{7}\times \left(7\right)\times \frac{35}{4}=192.5{\text{cm}}^2$