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 \\ (803.84)/(4\pi)=(4\pi* r^2)/(4\pi) \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}=(4)/(3)*3.14*8^3 \\ V=(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).