Question

The radius and height of a right circular cone are in the ratio $5:12$ and volume is $2512cm$, then find the curved surface area and the total surface area of the cone is

• A. $1140.33{cm}^2$
• B. $1150.42{cm}^2$
• C. $1130.56{cm}^2$
• D. $1125.59{cm}^2$

Answer 1

The correct option is C $1130.56{cm}^2$

Let the radius be 5x height be 12x

volume = 2512$c{m}^3$

volume of right circular cone =$\frac{1}{3}\pi r^{2}h$

$2512=\frac{1}{3}\times \frac{22}{7}\times 5x\times 5x\times 12x$

$\Rightarrow x^3=8$

$\Rightarrow x=2$

So radius = 10 cm height =24 cm

CSA=$\pi rl=\pi r\sqrt{{\pi }^2{h}^2}$

$\frac{22}{7}\times 10\sqrt{100+{24}^2}=816.4$

$TSA=CSA+\pi r^2$

=816.4+$\frac{22}{7}\times 10\times 10=1130.559$

=1130.56$c{m}^2$