Question

The radio of two cones in the ratio 2:1 their volumes are equal .find the ratio of their heights

Answer 1

SoluTion :-

Let their radii be 2x, x and their heights be h and H respectively

Then,

$\sf {Volume\ of\ cone = \frac{1}{3}\pi r^{2} h }\\\\\\\sf {\frac{\frac{1}{3}\times \pi (2x)^2 \times h }{\frac{1}{3} \times \pi \times x^2 \times H } }\\\\\\\sf {\Rightarrow \frac{h}{H}=\frac{1}{4} }\\\\\sf {\Rightarrow h:H}\\\\\sf {\Rightarrow 1:4}$