Question

a cylinder, whose height is two-thirds of its diameter, has the same volume as a sphere of radius 4 cm. calculate the radius of the base of the cylinder

Answer 1

$Let \: radius \: of \: cylinder \: be \: \: x \\ Then \: it's \: \: height \: = \frac{2}{3} \times 2x = \frac{4x}{3} \\ given \: \: volume \: of \: cylinder = volume \: of \: sphere \\ \pi \times {x}^{2} \times \frac{4x}{3} = \frac{4}{3} \times \pi \times {4}^{3} \\ {x}^{3} = {4}^{3} \\radius \: \: x = 4 \: cm$