We are told that the volume of a cube is 125 cubic inches. We want to find the length of its sides. Let's visualize the situation by drawing a cube and letting s be the length of its sides.
When we find the volume of a prism, we multiply its three side measurements — the length, the width, and the height — which all happen to be the same for a cube. Recall that multiplying a number by itself three times is equal to raising the number to the power of 3.
V= s* s* s ⇔ V= s^3
Since we already know that the volume is 125 cubic inches, we will substitute this value for V in the above equation. Then we can solve for s by taking the cube root of both sides of the equation. Let's do it!
The length of each side of a cube with a volume of 125 cubic inches is 5 inches.
To calculate the surface area of a prism, we can use the following formula.
S=2(l w+l h+wh)
The terms inside the parentheses represents the area of one of the three possibly different-sized faces. Each term is multiplied by 2 because opposite faces in a rectangular prism have equal dimensions. In our case, all the dimensions have the same length s because our prism is a cube.
S=2(s^2+s^2+s^2) → S=6s^2
This is the formula for the surface area of a cube. Since s=5, let's substitute this value into our new formula to calculate S.
