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:

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

Substitute the value of the volume:

$1928\pi=\frac{4}{3}\pi r^3$

Simplify:

$\begin{gathered} 1928\pi\cdot\frac{3}{4\pi}=\frac{4}{3}\pi r^3\cdot\frac{3}{4\pi} \\ \frac{5784}{4}=r^3 \\ r^3=1446 \end{gathered}$

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