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  • If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6: pi.

Direction: Write True or False and justify your answer in each of the following :

If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6:\pi.

 

Answers (1)

Answer: True

Explaination:

\\$ Volume of cube $\left(V_{1}\right)=(\text { Side })^{3}\\$ Radius of sphere $(r)=\frac{\text { Side }}{2}\\$ Volume of sphere $\left(V_{2}\right)=\frac{4}{3} \pi\left(r^{3}\right) \\ =\frac{4}{3} \pi\left(\frac{\text { Side }}{2}\right)^{3}\\=\frac{4}{3} \pi \times \frac{(\text { Side })^{3}}{8} \\ \frac{V_{1}}{V_{2}} =\frac{(\text { side })^{3}}{\frac{4}{3} \pi \frac{(\text { side })^{3}}{8}}=\frac{6}{\pi} \\\\ V_{1}:V_{2}=6: \pi

Posted by

Ravindra Pindel

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