Question

A sphere and a cylinder have the same radius, and the height of the cylinder is equal to its radius; which figure has the greater volume?

Answer 1

Answer:

The sphere has the greatest volume

Step-by-step explanation:

First note down the formula for volume of sphere and that for volume of a cylinder

Volume of a cylinder

$=\pi r^2h$

Volume of the sphere

$=\frac{4}{3} \pi r^3$

Now from the question, the radius of the cylinder and sphere are equal.In addition, the radius of cylinder is equal to its height.This means that the radius of the sphere, the radius of the cylinder and the height of the cylinder are all equal

Hence,

lets take the radius of cylinder to be= x units

The radius of the sphere will be =x units

The height of the cylinder will be= x units

Calculate the volume of cylinder

$V=\pi r^2h=\pi *x^2*x=\pi x^3$

Calculate the volume of the sphere

$V=\frac{4}{3} *\pi *r^3=\frac{4}{3} *\pi *x^3=\frac{4}{3} \pi x^3$

Comparing the volumes

The volume of the sphere is more than the volume of cylinder.If you take the value of x=1 then

Volume of sphere will = 4.189 cubic units

Volume of cylinder will= 3.142 cubic units