Given:
A sphere and a cylinder have the same radius and height.
The volume of the cylinder is 50 ft.
Required:
We need to find the volume of the sphere.
Explanation:
Let r be the radius of the sphere and cylinder.
Let h be the height of the sphere and cylinder.
We know that the height of the sphere is the diameter.
[tex]h=d=2r[/tex]
Consider the volume of the cylinder formula.
[tex]V=\pi r^2h[/tex]
Substitute V=50ft and h =2r in the formula.
[tex]50=\pi r^2(2r)[/tex][tex]50=2\pi r^3[/tex][tex]\text{ Divide both sides by }2\pi\text{ of the equation.}[/tex]
[tex]\frac{50}{2\pi}=\frac{2\pi r^3}{2\pi}[/tex][tex]\frac{25}{\pi}=r^3[/tex]
Consider the volume of the sphere formula.
[tex]V_1=\frac{4}{3}\pi r^3[/tex]
[tex]Substitute\text{ }r^3=\frac{25}{\pi}\text{ in the formula.}[/tex]
[tex]V_1=\frac{4}{3}\pi\times\frac{25}{\pi}[/tex][tex]V_1=\frac{100}{3}ft^3[/tex]
Final answer:
[tex]V_1=\frac{100}{3}ft^3[/tex]
