Question

A cube has a surface area of 253 1/2 square inches. What is the area of one

face of the cube in square inches? How do you know?

Answer 1

The area of one face of a cube with a total surface area of 253 1/2 square inches is 42 1/4 square inches. This is found by dividing the total surface area by 6, as a cube has six equal faces.

Step-by-step explanation:

To find the area of one face of a cube with a surface area of 253 1/2 square inches, we need to understand that a cube has six faces, and they are all identical in area. So, if the total surface area is 253 1/2 square inches, we divide this number by 6:

253 1/2 ÷ 6 = 42 1/4 square inches.

Therefore, each face of the cube has an area of 42 1/4 square inches. We know this because the surface area of a cube is calculated by the formula SA = 6 × s², where 's' is the length of one side of the cube, and since the cube has 6 equal faces, dividing the total surface area by 6 gives us the area of a single face.

Answer 2

The area of one face of the cube is approximately 1785.06 square inches. This is found by dividing the total surface area by 6, as a cube has 6 identical faces.

Step-by-step explanation:

Surface area of a cube: The surface area of a cube is calculated by adding the areas of its 6 faces. Since all faces are identical squares, we can find the area of one face and multiply it by 6.

Formula: The formula for the surface area of a cube with side length s is:

Surface Area = 6s^2

Given information: We know the total surface area of the cube is 253 1/2 square inches. We need to find the area of one face (s^2).

Solving for s^2:

Divide the total surface area by 6:

253 1/2 sq in / 6 = 42.25 sq in

This value represents the area of one face of the cube (s^2).

Final answer: Therefore, the area of one face of the cube is approximately 42.25 square inches, or 1785.06 square inches when rounded to two decimal places.