Question

What statement of the volume of the 2 shapes is correct

Answer 1

The volume of a sphere is given by the following formula

`V=(4)/(3)\pi r^3`

Where r represents the radius of the sphere. The diameter of our sphere is 12 inches. The radius is half of the diameter, therefore, the radius of our sphere is 6 inches. Using this radius value on our equation, we have

`V_S=(4)/(3)\pi(6)^3=(4)/(3)\pi\cdot216=288\pi`

The volume of a cylinder is given by the following formula

`V=\pi r^2h`

Where r represents the radius and h the height of the cylinder. The diameter of our cylinder is 10 inches. The radius is half of the diameter, therefore, the radius of our cylinder is 5 inches. The height is also given and it is 12 inches. Using those values on the formula, we have

`V_C=\pi\cdot(5)^2\cdot12=\pi\cdot25\cdot12=300\pi`

Comparing the volumes, we have

`300\pi>288\pi\Rightarrow V_C>V_S`

The volume of the cylinder is greater than the volume of the sphere.