Question

A solid sphere is cut into two hemispheres. From one, a square pyramid and from the other a cone, each of maximum possible size are carved out. What is the ratio of their volumes?

Answer 1

Volume of sphere = \(\frac{4}{3}\pi \times r^3\)

Volume of square pyramid cut from first hemisphere = \(\frac{1}{3}a^2h\)

= \(\frac{1}{3}\times(\sqrt{2}\,r)^2\times r=\frac{2r^3}{3}\)

Volume of cone cut from second hemisphere

Ratio of volumes

= \((2\frac{r^3}{3}):(\frac{1}{3}\pi r^3)\)

= \(\frac{2}{3}:\frac{1}{3}\pi\) = 2 : π