Question

The radius and the height of a right circular cone are in the ratio 5:12 and its volume is 2512cm cube. Find the CSA anf TSA of the cone.

Answer 1

Let the radius be 5x and the height be 12x.
Volume of cone = $\frac{1}{3}\pi r^{2}h$
$\Rightarrow 2512=\frac{1}{3}\times 3.14\times 5x\times 5x\times 12x$
$\Rightarrow 2512=3.14\times 5x\times 5x\times 4x$
$\Rightarrow 2512=3.14\times 100x^3$
$\Rightarrow \frac{2512}{314}=x^3$
$\Rightarrow x^3=8$
$\Rightarrow x=2$
Thus radius=5x=5×2=10 and
height=12x=12×2=24.
Now slant height $l=\sqrt{h^2+r^2}=\sqrt{{24}^2+{10}^2}=\sqrt{576+100}=\sqrt{676}=26$ cm
Now CSA of cone=$\pi rl=3.14\times 10\times 27=816.4c{m}^2$
TSA of cone=$\pi r^2+\pi rl$
=$(3.14\times 100)+(3.14\times 10\times 26)$
=$1130c{m}^2$