Question

the surface area of a sphere is 314.16 ft squared. What is the volume?

Answer 1

To solve this problem, we will determine the radius of the sphere using the formula for the SA, then we will use the radius to compute the volume of the sphere. ( We will omit the units to simplify the calculations).

The formula for the surface area of a sphere is:

$SA=4\pi r^2,$

where r is the radius of the sphere. Therefore,

$314.16=4\pi r^2.$

Solving the above equation for r, we get:

$\begin{gathered} \frac{314.16}{4\pi}=r^2, \\ \sqrt{\frac{314.16}{4\pi}}=r. \end{gathered}$

Therefore, the radius of the sphere is:

$r\approx5\text{ ft.}$

Now, the volume of a sphere is given by the following formula:

$V=\frac{4}{3}\pi r^3.$

Substituting the above value, we get:

$V\approx523.6\text{ ft}^3.$

Answer:

$523.6ft^3.$