To solve these problems, we'll perform calculations based on the geometric properties of a cube.
a. Cross Section Area:
When you slice through the center of a cube, you create a cross section that is a square with side lengths equal to the edge length of the cube. The area of a square is given by the formula [tex]\( \text{Area} = \text{side length}^2 \)[/tex].
For a cube with an edge length of 5 inches, the area [tex]\( A \)[/tex] of the cross section is:
[tex]\( A = 5 \text{ inches} \times 5 \text{ inches} = 25 \text{ square inches} \)[/tex].
So, the area of the cross section is 25 square inches.
b. Surface Area:
The surface area of a cube is calculated by the sum of the areas of all six faces. Each face is a square, and since all six faces are identical, the surface area [tex]\( SA \)[/tex] is given by the formula [tex]\( SA = 6 \times \text{(side length)}^2 \)[/tex].
With an edge length of 5 inches, the surface area is:
[tex]\( SA = 6 \times (5 \text{ inches})^2 = 6 \times 25 \text{ square inches} = 150 \text{ square inches} \)[/tex].
Therefore, the surface area of the cube is 150 square inches.
c. Volume:
The volume of a cube is given by the formula [tex]\( V = \text{side length}^3 \)[/tex]. This gives us the volume of the cube in cubic units.
For a cube with an edge length of 5 inches, the volume [tex]\( V \)[/tex] is:
[tex]\( V = 5 \text{ inches} \times 5 \text{ inches} \times 5 \text{ inches} = 125 \text{ cubic inches} \)[/tex].
Hence, the volume of the cube is 125 cubic inches.
