Question

The radius and the 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. $141c{m}^2$
• B. $142.5c{m}^2$
• C. $140.5c{m}^2$
• D. $192.5c{m}^2$

Answer 1

Answer: (D)

Let radius and height of cone be $4x$ & $3x$. Now, area of base $=154{cm}^2$

$\Rightarrow \pi r^2=154{cm}^2\Rightarrow \frac{22}{7}\times 4x\times 4x=154{cm}^2$

$\Rightarrow x^2=\frac{154\times 7}{22\times 16}=\frac{49}{16}\Rightarrow x=\frac{7}{4},\therefore r=4\times \frac{7}{4}=7cm$

$h=\frac{3\times 7}{4}=5.25cm,l=\sqrt{{\left(7\right)}^2+{\left(5.25\right)}^2}=8.75cm$

CSA of cone $=\pi rl=\frac{22}{7}\times 7\times 8.75=192.5{cm}^2$