Question

ratio of volumes of sphere and cone of same radius and heights is​

Answer 1

Answer:

let the diameter of the spheres be "d"

∴the radius of sphere = d/2

$volume \: of \: sphere = \frac{4}{3} \pi( \frac{d}{2} ) ^{3} = \frac{4}{3} \pi\frac{d}{8} ^{3} \\ \\ volume \: of \: cone \: = \frac{1}{3}\pi( \frac{d}{2})^{2} \times d = \frac{1}{3}\pi \frac{d} {4}^{3}$

RATIO OF THEIR VOLUMES ~~~

$\frac{4}{3} \pi\frac{d}{8} ^{3} : \frac{1}{3}\pi \frac{d} {4}^{3} \\ \frac{4}{3} \times \frac{1}{2} : \frac{1}{3} \\ = 2:3$

so the ratio will be 2:3

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