Question

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Please answer the question...

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Answer 1

height of cube =diameter of sphere

if height=h

volume of cube=h^3

volume of sphere=4/3*pi*r^3

r=h/2

volume of sphere=4/3*pi*(h/2)^3

ratio= volume of cube:volume of sphere

=h^3 : 4/3*pi*(h/2)^3

=6:pi

=6:22/7

Answer 2

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The sphere will have the diameter equal to the side of the cube as they are of the same height.

If the length of the side of the cube is a, then the diameter of the sphere  = a unit

•°• Radius of their sphere = a\2

$\huge{\boxed{\red{Volume \: of \: sphere = \frac{4}{3}\pi{r}^{3} } }}$

Hence , volume of this sphere

$= \frac{4}{3} × \pi × \frac{a}{2}^{3} \\ \\ </p><p>= \frac{\pi{a}^{3}}{6}$

Volume of a cube of edge = a³

Ratio of their volumes

$= \frac{\pi{a}^{3}}{6} : {a}^{3} \\ \\ =\frac{\pi}{6} : 1 \\ \\ = \frac{22}{6 × 7} : 1 \\ \\ =\frac{11}{21} : 1 \\ \\ = 11 : 21$

THE RATIO OF THEIR VOLUME ARE 11 : 21.