Name: Parts of a Cuboid
Uploaded: 2019-07-19
Duration: 5 min 14 s
Description: Take this quick lesson on learning everything you'll need to know about cuboids and their faces, edges and vertices. Check out this short video!

Question

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

Accepted Answer

Given that a sphere and a right circular cylinder of the same radius have equal volumes.

Volume of sphere $= \frac{4}{3} π r^{3}$

and volume of right circular cylinder $= π r^{2} h$

$∴ Volume of sphere = Volume of right circular cylinder [Given]$

$\Rightarrow \frac{4}{3} π r^{3} = π r^{2} h \Rightarrow h = \frac{4}{3} r$

Diameter of the cylinder exceeds its height by

$= 2 r - \frac{4}{3} r = \frac{2 r}{3}$

Percentage by which diameter of the cylinder exceeds its height

$= \frac{\frac{2 r}{3}}{\frac{4}{3} r} \times 100 = \frac{2 \times 3}{3 \times 4} \times 100 = 50 %$

$∴$ The percentage is $50 %$ .

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

Important Questions on Surface Areas and Volumes

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