Question

The formula for the volume of a sphere is V = jar", where Vis the volume and ris the radius. Solve the formula for r. and then use it to answer the question. The volume of a basketball is about 435 cubic inches. What is the radius of the basketball, to the nearest tenth of an inch? Use 3.14 for it. A. 4.5 inches B. 4.7 inches C. 4.3 inches D. 4.1 inches

Answer 1

We are given the formula as volume of a sphere as

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

we are to find the radius r give the volume of sphere to be 435 cubic inches

Therefore

`\begin{gathered} V=435in^3,\text{ } \\ r\text{ = ?} \\ \pi\text{ = 3.14} \end{gathered}`

This gives

`\begin{gathered} 435in^3\text{ =}(4)/(3)*3.14\text{ }* r^3 \\ 3\text{ }*435in^{\text{ 3}}\text{ = 4 }*3.14\text{ }* r^3 \\ 1305in^3=12.56r^3 \\ \text{divide both side by 12.56} \\ (1305in^3)/(12.56)=r^3 \\ r^3=103.90in^3 \\ \text{take cube root of both sides} \\ r\text{ = }\sqrt[3]{103.90in^3} \\ r\text{ = 4.70 in} \end{gathered}`

Therefore

The radius of the sphere is 4.7 inches