Question

A sphere,a cylinder and a cone have the same radius and same height.find the ratio of their volumes.(hint: diameter of the sphere is equal to the heights of the cylinder and cone.)

Answer 1

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Answer 2

To find:

The ratio of volume of sphere, the cylinder and the cone

Solution:

We know that,  

The “height of cylinder and cone” to the diameter of sphere is equal.  

Radius of sphere is equal to R, Diameter = 2r.

Height of the cylinder and Cone = h =2r (According to the given condition)

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

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

Volume of cone $=\frac{1}{3} \pi r^{2} h$

Such that,  

Volume of cylinder: Volume of sphere: Volume of cone  

$=\pi r^{2} h : \frac{4}{3} \pi r^{3} : \frac{1}{3} \pi r^{2} h$

$=\pi r^{2} 2 r : \frac{4}{3} \pi r^{3} : \frac{1}{3} \pi r^{2} 2 r$

$=2 : \frac{4}{3} : \frac{2}{3}$

$\mathrm{F}=1 : \frac{2}{3} : \frac{1}{3}$

=3 : 2 : 1

Therefore the expected ratio is 3:2:1.