Question

The radius and the height of a right circuilar cone are in the ratio 5:12 and the volume is 2512cm3 find the radius and slant height of the cone

Answer 1

Answer:-

Let the radius of the cone be 5x cm and height of the cone be 12x cm.

given,

Volume of the cone = 2512 cm³

We know that,

$volume \: of \: a \: cone \: = \frac{1}{3} \times \pi \times {r}^{2} \times h \\ \\ 2512 = \frac{1}{3} \times \frac{22}{7} \times 5x \times 5x \times 12x \\ \\ 2512 \times 7 = 2200 {x}^{3} \\ \\ {x}^{3} = \frac{2512 \times 7}{2200} \\ \\ {x}^{3} = 8 \: (approx.) \\ \\ x = \sqrt[3]{8} \\ \\ x = 2$

Therefore,

Radius (r) = 5x = 5(2) = 10 cm

Height (h) = 12x = 12(2) = 24 cm.