Question

a cylinder whose height is two third of it diameter has the same volume as a sphere of radius 4 cm calculate radius of base of cylinder

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Answer 1

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Answer 2

Answer:

Radius of base of cylinder = 4cm

Explanation:

Dimensions of a cylinder:

Let the radius of base of a cylinder = r cm

Diameter (d) = 2r cm

height (h ) = two third of diameter

= (2/3)d

= (2/3)×2r

h = 4r/3 cm ---(1)

We know that,

$\boxed { Volume \:of \:a \:cylinder = \pi r^{2}h}$

ii ) Dimensions of a sphere:

Radius(R) = 4 cm

We know that ,

$\boxed { Volume \:of \:a \:sphere =\frac{4}{3} \pi R^{3}}$

According to the problem given,

volume of the cylinder = Volume of the sphere

$\pi r^{2}h= \frac{4}{3} \pi R^{3}$

$\implies\pi \times r^{2}\times\frac{4r}{3}=</p><p>\frac{4}{3} \pi R^{3}$

$\implies\frac{4}{3}\pi \times r^{3}=</p><p>\frac{4}{3} \pi R^{3}$

$\implies r^{3}=</p><p>\frac{\frac{4}{3} \pi R^{3}}{\frac{4}{3}\pi}$

After cancellation, we get

$\implies r^{3} = R^{3}$

Substitute R = 4 , we get

$\implies r^{3}=4^{3}$

$\implies r = 4\: cm$

Therefore,

Radius of base of cylinder = 4cm

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