Question

A ball has a volume of 142 cubic centimeters. What is the diameter of the ball?Show all work and round to the nearest tenth.

Answer 1

A ball has the shape of a sphere. So, to find the diameter of the ball, we would make use of the formula for finding the volume of a sphere.

`\begin{gathered} \text{Volume of a sphere V = }(4)/(3)*\pi* r^3^{}^{} \\ \text{Where r = the radius. } \\ \text{From } \\ \text{ V = }(4)/(3)*\pi* r^3 \\ 142\pi=\text{ }(4)/(3)*\pi* r^3 \\ \\ \text{Cancelling out the }\pi\text{ in both sides of the equation, we have } \\ 142=\text{ }(4)/(3)* r^3 \\ \\ 142=\text{ }(4r^3)/(3) \\ \\ \text{Cross multipying we have } \\ 4r^3=142*3 \\ 4r^3=426 \\ r^3=(426)/(4) \\ \\ r^3=106.5 \\ r=\sqrt[3]{106.5} \\ \\ r=4.74 \\ \text{Diameter = 2 x radius } \\ \text{Diameter}=\text{ 2}*4.74 \\ \text{Diameter =9.48} \\ \text{Diameter = 9.5 to the nearest 10th} \end{gathered}`