Question

The sphere has volume $\frac{9}{4}$ times of cylinder volume. The cylinder height is 2 times of its radius. How many times does the surface area of cylinder has when compare with surface area of sphere?

Answer 1

Let the radius of the sphere be r .

Then the height of the cylinder is 2 r .

Volume of cylinder = π r² h

⇒ π r² × 2 r

⇒ 2 π r³

The volume of the cylinder is 2 π r³ .

The volume of sphere is 9/4 × 2 π r³

⇒ 9/2 π r³

We know that the volume of sphere is 4/3 π r³ .

So 4/3 π R³ = 9/2 π r³ on taking the radius as R .

⇒ R³ = 27/8 r³

⇒ R = 3/2 r

Hence radius of sphere is 3/2 r .

Surface area of sphere = 4 π R² .

Surface area of cylinder = 2 π r ( h + r )

Comparison :-

$\dfrac{2\pi r(h+r)}{4\pi R^2}\\\\\implies \dfrac{2\pi r(2r+r)}{4\pi\times\dfrac{3r}{2}}\\\\\implies \dfrac{3r}{3r}\\\\\implies 1$

Hence the surface areas of both the objects will be the same .