A manufacturer wants to produce a 4"× 2"× 5"
rectangular box to hold teabags using the net shown.
Study the box and the net.
Then complete the statements below to find the surface area of the box.
To find the surface area of the box, we need to calculate the area of each face of the box using the given dimensions.
The dimensions of the box are:
- Length: 4 inches
- Width: 2 inches
- Height: 5 inches
1. There are two rectangles that make up the top and bottom faces of the box. The dimensions of each rectangle are 4 inches by 2 inches. Therefore, the area of each rectangle is (4 inches) * (2 inches) = 8 square inches. Since there are two of these rectangles, their total area is 8 square inches * 2 rectangles = 16 square inches.
2. There are two rectangles that make up the front and back faces of the box. The dimensions of each rectangle are 4 inches by 5 inches. Therefore, the area of each rectangle is (4 inches) * (5 inches) = 20 square inches. Since there are two of these rectangles, their total area is 20 square inches * 2 rectangles = 40 square inches.
3. There are two rectangles that make up the left and right faces of the box. The dimensions of each rectangle are 2 inches by 5 inches. Therefore, the area of each rectangle is (2 inches) * (5 inches) = 10 square inches. Since there are two of these rectangles, their total area is 10 square inches * 2 rectangles = 20 square inches.
Finally, to find the total surface area of the box, we sum up the areas of all the faces:
16 square inches + 40 square inches + 20 square inches = 76 square inches.
Therefore, the surface area of the box is 76 square inches.