Question
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
222 in.2
222 in. squared
120 in.2 120 in. squared
228 in.2
228 in. squared
234 in.2
Step 1: Calculate the surface area of the cab section (rectangular prism on the left)
The cab section has dimensions width = 2 inches, height = 3 inches, and depth = 3 inches.
Surface area of a rectangular prism = 2(width x height + height x depth + width x depth)
Surface area of cab = 2(2x3 + 3x3 + 2x3) = 2(6 + 9 + 6) = 2(21) = 42 square inches
Step 2: Calculate the surface area of the shipping container section (rectangular prism on the right)
The shipping container section has dimensions width = 9 inches (11 total length - 2 cab width), height = 6 inches, and depth = 3 inches.
Surface area of shipping container = 2(9x6 + 6x3 + 9x3) = 2(54 + 18 + 27) = 2(99) = 198 square inches
Step 3: Add the surface areas of the cab and shipping container to find the total surface area of the truck.
Total surface area = Surface area of cab + Surface area of shipping container
Total surface area = 42 square inches + 198 square inches
Total surface area = 240 square inches
Therefore, the total surface area of the truck (excluding the wheels) is 240 square inches.
Answer: 240 in.2 or 240 in. squared