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:The sphere has the greatest volumeStep-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 equalHence, lets take the radius of cylinder to be= x unitsThe radius of the sphere will be =x unitsThe height of the cylinder will be= x unitsCalculate 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 volumesThe 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