Question

A cylinder with height equal to its diameter has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder correct to one decimal place.

Answer 1

Answer :

Let height of cylinder = h
And
Diameter = d
And
Radius = r
We know d = 2r
From question we get

d = h
So,
h = 2r ---------- ( 1 )

We know Volume of cylinder = $\pi$r²h
And
Radius of sphere = 4 cm
And
Volume of Sphere = $\frac{4\pi r^3}{3}$ , So
Here volume of sphere = $\frac{4\times \pi \times 4^3}{3}$
And as given volume of cylinder and sphere is equal , So

$\pi$r²h = $\frac{4\times \pi \times 4^3}{3}$

Substitute value from equation 1 , we get

$\pi$r² ( 2r ) = $\frac{4\times \pi \times 4^3}{3}$

2$\pi$r³ = $\frac{4\times \pi \times 4^3}{3}$

r³ = $\frac{2\times 4^3}{3}$

r = $\sqrt[3]{\frac{2\times 4^3}{3}}=4\sqrt[3]{\frac{2}{3}}=4\times 0.87358=3.49432\mathbf{=}\mathbf{}\mathbf{}\mathbf{3}\mathbf{.}\mathbf{5}\mathbf{}\mathit{c}\mathit{m}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathit{A}\mathit{n}\mathit{s}\mathbf{}\mathbf{)}$