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
[tex]=\pi r^2h[/tex]
Volume of the sphere
[tex]=\frac{4}{3} \pi r^3[/tex]
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
[tex]V=\pi r^2h=\pi *x^2*x=\pi x^3[/tex]
Calculate the volume of the sphere
[tex]V=\frac{4}{3} *\pi *r^3=\frac{4}{3} *\pi *x^3=\frac{4}{3} \pi x^3[/tex]
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
