A cardboard box has a square base and a square top. The height of the box is 13 inches. Express the surface area A (the sum of the areas of all six sides of the box) in terms of the length l of the box.
Can someone please help me
top = L^2
bottom = L^2
4 sides = 4*13L
total = 2 L^2 + 52 L
Certainly! To find the surface area of the cardboard box, we need to consider all six sides. Let's break down the sides of the box:
1. The base and top: Since they are both square, each will have an area of l * l = l^2.
2. The four sides: These are the vertical faces of the box. Each side will have an area equal to the product of the length of the side, l, and the height of the box, which is given as 13 inches. So, each side will have an area of 13 * l = 13l.
Now, let's calculate the total surface area (A) of the box:
The two square bases will contribute 2 * l^2 to the surface area.
The four sides will contribute 4 * 13l to the surface area.
Therefore, the total surface area A of the box is: A = 2 * l^2 + 4 * 13l.
So, the expression for the surface area in terms of the length 'l' of the box is: A = 2l^2 + 52l.