Question

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

• A. $192.5c{m}^2$
• B. $195c{m}^2$
• C. $190.5c{m}^2$
• D. $185.5c{m}^2$

Answer 1

Answer: (A)

$192.5c{m}^2$

Given, ratio of radius and height of cone is $4:3:$.

Then, let radius be $4x$ and height be $3x$.

We know, the base of a cone is a circle.

$\therefore$ Area of base $=$ $\pi r^2=154\Rightarrow \frac{22}{7}\times {\left(4x\right)}^2=154$

$\Rightarrow 16x^2=\frac{154\times 7}{22}\Rightarrow x^2=\frac{49}{16}\Rightarrow x=\frac{7}{4}$.

$\therefore$ Radius $=$ $4\times \frac{7}{4}=7cm,$ and height $=3\times \frac{7}{4}=\frac{21}{4}=5.25cm$.

Now, curved surface area of cone $=$ $\pi rl$ and $l=\sqrt{r^2+h^2}=\sqrt{49+{\left(5.25\right)}^2}=8.75cm.$

$\therefore$ Curved surface area $=$ $\frac{22}{7}\times 7\times 8.75=192.5{cm}^2$.

Hence, option $A$ is correct.