find the smallest rectangular area of wrapping paper that can be used to wrap a present that is 22 inches by 20 inches by 10 inches. The paper cannot be cut.
To find the smallest rectangular area of wrapping paper that can be used to wrap the present without cutting, we need to calculate the surface area of the present.
The surface area of a rectangular box can be calculated by summing the areas of all its faces. For this present, we have six faces: the top, bottom, front, back, left, and right sides.
Let's calculate the area of each face first:
- The top and bottom faces have dimensions 22 inches by 20 inches. So, the area of each is (22 inches) * (20 inches) = 440 square inches.
- The front and back faces have dimensions 22 inches by 10 inches. So, the area of each is (22 inches) * (10 inches) = 220 square inches.
- The left and right faces have dimensions 20 inches by 10 inches. So, the area of each is (20 inches) * (10 inches) = 200 square inches.
Now, let's sum up the areas of all the faces to get the total surface area of the present:
440 square inches (top) + 440 square inches (bottom) + 220 square inches (front) + 220 square inches (back) + 200 square inches (left) + 200 square inches (right) = 1520 square inches.
Therefore, the smallest rectangular area of wrapping paper needed to wrap the present without cutting is 1520 square inches.
As = 2(L*W) + 2(L*h) + 2(W*h)
As = 2(22*20) + (2(22*10) + 2(20*10) = Surface area.