Question

Find the surface area and volume of the sphere. Round your answers to the nearest whole number.C = 4 in.The surface area is aboutsquare inchesThe volume is aboutcubic inches

Answer 1

The circumference of a sphere with radius r is given by the following formula:

`C=2\pi r`

Isolate r from the equation and substitute the value of C to find the raius of the sphere:

`\begin{gathered} \Rightarrow r=(C)/(2\pi) \\ \Rightarrow r=\frac{4\pi\text{ in}}{2\pi} \\ \Rightarrow r=2\text{ in} \end{gathered}`

The surface area of a sphere with radius r is given by:

`S=4\pi r^2`

The volume of a sphere with radius r is given by:

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

Substitute r=2 in on each formula to find the volume and surface area of the sphere:

`\begin{gathered} S=4\pi(2in)^2 \\ =4\pi\cdot4in^2 \\ =16\pi in^2 \\ =50.26\ldots in^2 \\ \approx50in^2 \end{gathered}`