Question

The volume of a sphere is 1928 m3. What is the surface area of the sphere to the nearest tenth? 2 24.228 m 142.1 m² 1606.9 m² 803.4 m2

Answer 1

Given:

volume = 1928π m^3

And the formula of the volume for the sphere is:

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

Substitute the value of the volume:

`1928\pi=(4)/(3)\pi r^3`

Simplify:

`\begin{gathered} 1928\pi\cdot(3)/(4\pi)=(4)/(3)\pi r^3\cdot(3)/(4\pi) \\ (5784)/(4)=r^3 \\ r^3=1446 \end{gathered}`

And solve for r:

`r=\sqrt[3]{1446}=11.31`

Next, the surface area is given by:

`SA=4\pi r^2`

Substitute the values:

`SA=4(3.14)(11.31)^2=1606.9`

Answer: 1606.9 m^2