A solid sphere whose radius is 21 cm is melted and recast into a regular pyramid of the square base. If the height of the pyramid is 66 cm, then what is the length of each side of the base of the pyramid? [Use $$\pi = \frac{22}{7}$$ ]

Volume of sphere = Volume of a regular pyramid of the square base

$$\frac{4}{3}\times\ \pi\ \times\ \left(radius\right)^3\ =\ \frac{length\times width\times height\ \ }{3}$$

As we know that the pyramid has a square base and the length and width of a square is the same.

$$\frac{4}{3}\times\ \pi\ \times\ \left(radius\right)^3\ =\ \frac{length\ of\ side\times length\ of\ side\times height\ \ }{3}$$

A solid sphere whose radius is 21 cm. If the height of the pyramid is 66 cm.

$$\frac{4}{3}\times\ \frac{22}{7}\times\ 21\times\ 21\times\ 21\ =\ \frac{\left(length\ of\ side\right)^2\times66\ }{3}$$

$$4\times\ 21\times\ 21\ =\ \left(length\ of\ side\right)^2\times1$$

The length of each side of the base of the pyramid = 42 cm