Question

The volume of a sphere with radius r is given by the formula ___Find the volume of a sphere with diameter 40 inches. Round to two decimal places.

Answer 1

The radius of a circle is half the length of its diameter. Then, the radius of this sphere is 20 inches because:

`\begin{gathered} \text{Radius }=\frac{\text{ Diameter}}{2} \\ \text{Radius }=(40in)/(2) \\ \text{Radius }=20in \end{gathered}`

Now, using the given formula to find the volume of a sphere with radius r, we have:

`\begin{gathered} V=(4)/(3)\pi r^3 \\ V=(4)/(3)(3.141592)(20in)^3 \\ V=(4)/(3)(3.141592)(20^3)in^3 \\ V=(4)/(3)(3.141592)(8000)in^3 \\ $$\boldsymbol{V=33,510.32in}^{\boldsymbol{3}}$$ \end{gathered}`

Therefore, the volume of a sphere with a diameter of 40 inches rounded to two decimal places is 33,510.32 cubic inches.