Question

a solid metal cube with an edge length of 9 inches is melted down and reshaped into a sphere. which of the following is the surface area of the sphere to the nearest tenth of an inch

Answer 1

would the length of the edge be the diameter of the sphere? or would it be the radius?

Answer 2

volume of cube=9^3=9*9*9=729
volume of sphere=729 cubic inches.
Let r be the radius of sphere.
Then
\[\frac{ 4 }{ 3 } \pi r^3=729\] find r
surface area of sphere\[=4 \pi r^2=?\]

Answer 3

Sorry I went to work last night. So to solve for r would you divide 729by pi first?

Answer 4

@surjithayer

Answer 5

\[r^3=729 \times \frac{ 3 }{ 4 \pi }=\frac{ 2187 }{ 4 \pi }\]
\[r=\left( \frac{ 2187 }{ 4 \pi } \right)^{\frac{ 1 }{ 3 }}\]
\[Surface~area=4 \pi~\times \left\{ \left( \frac{ 2187 }{ 4 \pi } \right)^{\frac{ 1 }{ 3 }} \right\}^2=?\]