Use the image to answer the question.
An illustration shows a 3-dimensional line diagram of a truck that appears as two adjoining rectangular prisms placed on two visible wheels. The rectangular prism on the left, representing the cab section of the truck, has a height of 3 inches and a horizontal length of 2 inches. The rectangular prism on the right, or the cargo section, is 6 inches high. The back of the truck is marked as 3 inches deep. The total horizontal length of the two prisms combined is 11 inches.
A toy truck is comprised of a rectangular cab and a shipping container that it is carrying. What is the total surface area of the truck (excluding the wheels)?
To find the total surface area of the truck (excluding the wheels), we need to calculate the surface area of each individual prism and then add them together.
1. Surface area of the cab section:
- The front and back faces of the cab section each have an area of 2 inches x 3 inches = 6 square inches.
- The top and bottom faces have areas of 2 inches x 2 inches = 4 square inches each.
- The two side faces have areas of 3 inches x 2 inches = 6 square inches each.
- Therefore, the total surface area of the cab section is: 6 + 6 + 4 + 4 + 6 + 6 = 26 square inches.
2. Surface area of the cargo section:
- The front and back faces of the cargo section each have an area of 2 inches x 6 inches = 12 square inches.
- The top and bottom faces have areas of 6 inches x 3 inches = 18 square inches each.
- The two side faces have areas of 3 inches x 3 inches = 9 square inches each.
- Therefore, the total surface area of the cargo section is: 12 + 12 + 18 + 18 + 9 + 9 = 78 square inches.
3. Total surface area of the truck (excluding the wheels):
- Adding the surface areas of the cab and cargo sections together: 26 + 78 = 104 square inches.
Therefore, the total surface area of the toy truck (excluding the wheels) is 104 square inches.