Question

A sphere has a surface area of about803.84 square centimeters. What is the volumeof the sphere? Use 3.14 for (pie)and round to thenearest whole number.

Answer 1

Write out the formula for the Surface area of a sphere

$\text{Surface area of a sphere=4}\pi r^2$

Substitute the value for the surface area and solve for the radius.

$\begin{gathered} 803.84=4\pi r^2 \\ \pi=3.14 \\ \frac{803.84}{4\pi}=\frac{4\pi\times r^2}{4\pi} \end{gathered}$$\begin{gathered} r^2=\frac{803.84}{4\times3.14}=64 \\ r=\sqrt[]{64} \\ r=8\operatorname{cm} \end{gathered}$

Formula for the volume of a sphere

$\begin{gathered} \text{Volume of a sphere=}\frac{\text{4}}{3}\pi r^3 \\ \text{where r=8, }\pi=3.14 \\ \text{Volume}=\frac{4}{3}\times3.14\times8^3 \\ V=\frac{6430.72}{3}=2143.5733\approx2144cm^3(\text{nearest whole number)} \end{gathered}$

Hence, the volume of the sphere is 2144cm³(to the nearest whole number).