Question

The volume of a sphere is 3,000π m3. What is the surface area of the sphere to the nearest square meter

Answer 1

\[V_{sphere} = \frac{ 4 }{ 3 } \pi r^{3}\]
\[A_{sphere} = 4 \pi r^2\]

Answer 2

They give you the volume, thus you can solve for the radius. Once you solve for the radius, you can solve for the surface area.

Answer 3

\[V_{sphere} = \frac{ 4 }{ 3 } \pi r^{3}\]
\[3000 \pi = \frac{ 4 }{ 3 } \pi r^{3}\]
Divide by pi on both sides, then multiple by 3/4 on both sides (objective: to remove pi and the 4/3 fraction. Remember, we are solving for the radius)
\[(\frac{ 3 }{ 4}) 3000 = \frac{ 4 }{ 3 } r^{3} \times (\frac{ 3 }{ 4 })\]
\[2250 = r^{3}\]
\[r = \sqrt[3]{2250} = 13.1\]
\[A_{sphere} = 4 \pi r^2\]
\[A_{sphere} = 4 \pi (13.1)^{2}\]
\[A_{sphere} = 2158m^{2}\]