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)?
(1 point)
Responses
234 in.2 234 in. squared
222 in.2
222 in. squared
120 in.2 120 in. squared
228 in.2
228 in. squared
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To find the total surface area of the truck (excluding the wheels), we need to calculate the surface area of both the cab and the cargo section, and then add them together.
Surface area of the cab:
The cab is in the shape of a rectangular prism with dimensions 3 inches (height), 2 inches (length), and 3 inches (depth).
Surface area = 2lw + 2lh + 2wh
= 2(2*3) + 2(3*3) + 2(2*3)
= 12 + 18 + 12
= 42 square inches
Surface area of the cargo section:
The cargo section is also in the shape of a rectangular prism with dimensions 6 inches (height), 9 inches (length, combined total of the cab and cargo sections), and 3 inches (depths, which is also the same depth as the cab section).
Surface area = 2lw + 2lh + 2wh
= 2(9*6) + 2(6*3) + 2(9*3)
= 108 + 36 + 54
= 198 square inches
Total surface area of the truck (excluding the wheels):
42 (cab) + 198 (cargo) = 240 square inches
So, the total surface area of the truck (excluding the wheels) is 240 square inches.