Find the surface area of a cube that has a volume of 512 in.?

Answer 1

Simple:

Correction: Volume should be in Cubic Units ie., = 512 inch ^3

First take a note. We are going to use the following 2 formulae

1. Volume of a cube of side 's' units = s ^3 cubic units

2. The surface area of a Cube of side 's' units = 6 * (s) ^ 2 sq. units

The Volume of the Cube = 512 cubic inches

The side of the Cube = Cube root of 512

= cube root of ( 8 * 8 * 8 )

= 8 inches.

Surface area of the Cube of side 's' = 6 (s) ^ 2

= 6 * 8 * 8

= 384 sq. inches Answer

Is it clear?

Use a diagram of cube for better understanding.

Answer 2

Take the cube root of 512, which is 8 inches.
Then multiply 8 x 8 to get the area of each face, which is 64.
Finally, multiply the area by the 6 faces of cube. (64 x 6 = 384 inches squared.)

Answer 3

A cube with a volume of 512 cubic inches, your problem says in. and that makes no sense, has one side the cube root of 512 that is 8.
So one side of the cube has an area of 8in. times 8in or 64 sq in.
A cube has six sides so 64 sq in times 6 equals 384 sq in

Answer 4

length of side = 512^(1/3) = 8 inches
Surface area = 6 x 8² ins ²
Surface area = 384 in ²

Answer 5

Let the side of the cube be x

x^3 = 512
x = 8 inches (Taking cuberoot of both sides)

Total Surface Area (TSA) = 6x^2
= 6*64
= 384 sq. inches

Lateral Surface Area (LSA) = 4x^2
= 4 * 64
= 256 sq. inches

TSA is the area occupied by all the six faces
LSA is the area occupied by the four standing face (the 'walls')