Question

A sphere of radius 4 cm has the same volume
as that of a cone with the same radius The
height of the cone will be​

Answer 1

Answer:

height of cone is 16cm

Step-by-step explanation:

given,

sphere

radius=4cm

$volume= \frac{4}{3} \pi {r}^{3} \\ = \frac{4}{3} \pi {4}^{3} = \frac{ {4}^{4} }{3} \pi {cm}^{3}$

cone

radius=4cm

$volume = \frac{1}{3} \pi {r}^{2} h \\ = \frac{1}{3} \pi {4}^{2} h = \frac{ {4}^{2} }{3} \pi \: h \: \: {cm}^{2}$

according to problem

volume of sphere = volume of cone

so,

$\frac{ {4}^{4} }{3} \pi = \frac { {4}^{2} }{3} \pi \: h \\ \frac{ {4}^{4} }{ {4}^{2} } = h \\ h = 16cm$

hence height of cone is 16cm