Question

a sphere and a cube have the same height find the ratio of their volume

Answer 1

Answer:

$\purple{ \mathsf{\fcolorbox{violet}{lightskyblue}{a sphere and a cube have the same height }}} \\ \purple{ \mathsf{\fcolorbox{violet}{lightskyblue}{ find the ratio of their volume}}}$

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 the sphere =

$\frac{2}{a}$

Volume of a sphere of radius 'r' =

$\frac{4}{3} \pi {r}^{3}$

Hence, volume of this sphere =

$\frac{4}{3} \times \pi \times {(\dfrac{a}{2})}^{3} \\ = \frac{ {\pi a}^{3} }{6}$

Volume of a cube of edge a =

${a}^{3}$

Ratio of their volumes =

$\frac{{\pi a}^{3}}{6} : {a}^{3} \\ \\ = \frac{\pi}{6} : 1 \\ \\ = \frac{22}{7 \times 6} : 1 \\ \\ = { \color{white}{ \fcolorbox{pink}{grey}{11 : 21}}}$