A sphere and a right circular cylinder of the same radius have equal volumes By what percentage does the diameter - Maths - Surface Areas and Volumes

Question

A sphere and a right circular cylinder of the same radius have
equal volumes By what percentage does the diameter of the cylinder
exceed its height

Ankush Jain · Accepted Answer

Let the equal radius of both sphere and cylinder be r and height of the cylinder be r.

Given, volume of cylinder = volume of sphere

$\Rightarrow π r^{2} h = \frac{4}{3} π r^{3} \Rightarrow h = \frac{4}{3} r \Rightarrow 2 r = \frac{3 h}{2} \Rightarrow D = \frac{3 h}{2} [w h e r e D b e t h e d i a m e t e r o f t h e c y l i n d e r]$

Now, let h be 100 %.

$∴ D = \frac{3 h}{2} = \frac{3}{2} \times 100 % = 150 %$

So, required difference = 150% - 100% = 50%

Hence, diameter of the cylinder exceed its height by 50%.

A sphere and a right circular cylinder of the same radius have equal volumes.By what percentage does the diameter of the cylinder exceed its height