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 to the nearest tenth of an inch
90.5 sq in
254.5 sq in
391.7 sq in
574.8 sq in

Answer 1

First, we need to find the volume of the cube which is:

9^3 = 729 cubic inches

Since this metal is melted down and reshaped into a sphere, the volume remains the same. Therefore, we can use the formula for the volume of a sphere:

V = (4/3)πr^3

729 = (4/3)πr^3

r^3 = (729 x 3) / (4π)

r^3 ≈ 206.36

r ≈ 6.41

Now, we can use the formula for the surface area of a sphere:

A = 4πr^2

A ≈ 514.7 sq in

Rounded to the nearest tenth, the surface area is 514.7 sq in.

Therefore, the closest answer choice is 574.8 sq in.