Question

What is the base area of a cube of volume 125 cubic units?

Base area = ______ sq. units.

Answer 1

25 square units.

Explanation:

If a cube has a volume of 125 cubic units, then the edge length of the cube is the cube root of 125:

edge length = ∛125 = 5

Since all sides of a cube are equal, the base of the cube is a square with sides of length 5 units. The area of a square is calculated by multiplying the length of one side by itself:

base area = 5 × 5 = 25 sq. units.

Therefore, the base area of the given cube is 25 square units.

Answer 2

Answer: The base area of the cube is 25 square units.

Step-by-step explanation: A cube has six square faces, all of which are identical. The base area of a cube refers to the area of one of these square faces.

The formula for the volume of a cube is:

V = s^3

where V is the volume of the cube and s is the length of one side of the cube.

If we know the volume of the cube is 125 cubic units, we can solve for the side length:

125 = s^3

Taking the cube root of both sides, we get:

s = 5

Therefore, each side of the cube has a length of 5 units. The area of one of the square faces of the cube is:

A = s^2

A = 5^2

A = 25 square units

So the base area of the cube is 25 square units.