Question

The radius and height of a circular cone are in ratio 5;12. If it's volume is 314 cm .Find its slant height. Using pie value is (3.14)

Answer 1

Volume of the circuler cone =
$\frac{1}{3}\pi {r}^{2} h$
$314 = \frac{1}{3} \times 3.14 \times {(5x)}^{2} \times 12x$
$\frac{314}{3.14 } = \frac{1}{3} \times {25x} \times 12x$
$100 \times 3 = 300 {x}$
$\frac{300}{300} = {x}$
$1 = {x}$
5x=5×1=5cm
12x=12×1=12cm
slant height =
$\sqrt{ {h}^{2} + {r}^{2} }$
$\sqrt{ {12}^{2} + {5}^{2} }$
$\sqrt{144 + 25}$
$\sqrt{169}$
$13cm$