A toy truck is compromise of a rectangular cab and a shipping container that it is carrying. What is the total surface area of the truck excluding the wheels. 11in long,3in wide,6in height,2in front, 3in
You can only pick from 222, 234, 120 and 228
To calculate the total surface area of the truck, we need to find the surface area of the cab and the shipping container separately and add them up.
Surface area of the cab:
The cab is a rectangular solid with dimensions 11in long, 3in wide, and 2in high. To find the surface area, we use the formula: SA = 2lw + 2lh + 2wh, where l = 11in, w = 3in, and h = 2in.
SA of cab = 2(11x3) + 2(11x2) + 2(3x2) = 66 + 44 + 12 = 122 in^2
Surface area of the shipping container:
The shipping container is also a rectangular solid with dimensions 11in long, 3in wide, and 4in high (subtracting the height of the cab from the overall height of the truck). It also has a front face that is 3in wide and 4in high.
Front face area = lw = 3x4 = 12 in^2
Remaining faces area = 2lw + 2lh + 2wh = 2(11x3) + 2(11x4) + 2(3x4) = 66 + 88 + 24 = 178 in^2
Total surface area of shipping container = front face area + remaining faces area = 12 + 178 = 190 in^2
Total surface area of the truck = SA of cab + SA of shipping container = 122 + 190 = 312 in^2
Therefore, the total surface area of the truck excluding the wheels is 312 square inches.
To find the total surface area of the truck, we need to calculate the surface areas of the individual components and then add them together.
1. The cab:
- The front face has dimensions 2 inches by 3 inches, so its area is 2 inches * 3 inches = 6 square inches.
- The two side faces have dimensions 6 inches by 6 inches, so each face has an area of 6 inches * 6 inches = 36 square inches.
- The top face has dimensions 6 inches by 3 inches, so its area is 6 inches * 3 inches = 18 square inches.
- The back face is not visible, so we exclude its area.
Therefore, the total surface area of the cab is 6 square inches + 36 square inches + 36 square inches + 18 square inches = 96 square inches.
2. The shipping container:
- The front face has dimensions 6 inches by 3 inches, so its area is 6 inches * 3 inches = 18 square inches.
- The back face is not visible, so we exclude its area.
- The bottom face has dimensions 6 inches by 11 inches, so its area is 6 inches * 11 inches = 66 square inches.
- The two side faces have dimensions 3 inches by 11 inches, so each face has an area of 3 inches * 11 inches = 33 square inches.
Therefore, the total surface area of the shipping container is 18 square inches + 66 square inches + 33 square inches + 33 square inches = 150 square inches.
To find the total surface area of the truck, we simply add the surface areas of the cab and the shipping container:
96 square inches + 150 square inches = 246 square inches.
So, the total surface area of the toy truck excluding the wheels is 246 square inches.