To calculate the total surface area of the truck, you need to find the surface area of the cab and the shipping container separately, and then add them together.
1. Surface area of the rectangular cab:
Since a rectangle has 4 sides, the surface area of the cab is 2 times the sum of the areas of the two sides (length x width) and the front (length x height).
Surface area of cab = 2lw + lh
Given that the cab has dimensions of 3 x 11 x 3:
Surface area of cab = 2(3)(11) + (3)(3)
Surface area of cab = 66 + 9 = 75 in^2
2. Surface area of the shipping container:
Since a rectangular prism has 6 faces, the total surface area is the sum of the surface areas of all 6 faces (2 of each dimension).
Given that the container is a rectangular prism with dimensions 11 x 3 x 6:
Surface area of container = 2lw + 2lh + 2wh
Surface area of container = 2(11)(3) + 2(11)(6) + 2(3)(6)
Surface area of container = 66 + 132 + 36 = 234 in^2
Now, add the surface areas of the cab and the container together:
Total surface area of the truck = Surface area of cab + Surface area of container
Total surface area of the truck = 75 + 234 = 309 in^2
Therefore, the total surface area of the truck (excluding the wheels) is 309 in^2.
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)? 3,11,3,6,2,
(1 point)
Responses
234 in.2 234 in. squared
120 in.2 120 in. squared
228 in.2
228 in. squared
222 in.2
5 answers
just the truck
I apologize for the confusion. Let's calculate the total surface area of just the toy truck (excluding the wheels).
1. Surface area of the rectangular cab:
Surface area of cab = 2lw + lh
Given that the cab has dimensions of 3 x 11 x 3:
Surface area of cab = 2(3)(11) + (3)(3)
Surface area of cab = 66 + 9 = 75 in^2
2. Surface area of the shipping container:
Surface area of container = 2lw + 2lh + 2wh
Given that the container is a rectangular prism with dimensions 11 x 3 x 6:
Surface area of container = 2(11)(3) + 2(11)(6) + 2(3)(6)
Surface area of container = 66 + 132 + 36 = 234 in^2
Now, add the surface area of the cab and the container together:
Total surface area of just the truck = Surface area of cab + Surface area of container
Total surface area of just the truck = 75 + 234 = 309 in^2
Therefore, the total surface area of just the truck (excluding the wheels) is 309 square inches.
1. Surface area of the rectangular cab:
Surface area of cab = 2lw + lh
Given that the cab has dimensions of 3 x 11 x 3:
Surface area of cab = 2(3)(11) + (3)(3)
Surface area of cab = 66 + 9 = 75 in^2
2. Surface area of the shipping container:
Surface area of container = 2lw + 2lh + 2wh
Given that the container is a rectangular prism with dimensions 11 x 3 x 6:
Surface area of container = 2(11)(3) + 2(11)(6) + 2(3)(6)
Surface area of container = 66 + 132 + 36 = 234 in^2
Now, add the surface area of the cab and the container together:
Total surface area of just the truck = Surface area of cab + Surface area of container
Total surface area of just the truck = 75 + 234 = 309 in^2
Therefore, the total surface area of just the truck (excluding the wheels) is 309 square inches.
including the wheels
To calculate the total surface area of the truck, including the wheels, we need to consider the surface area of all components. The total surface area would consist of the surface area of the cab, the shipping container, and the wheels.
1. Surface area of the cab:
Given that the cab has dimensions of 3 x 11 x 3:
Surface area of the cab = 2lw + lh
Surface area of the cab = 2(3)(11) + (3)(3)
Surface area of the cab = 66 + 9 = 75 in^2
2. Surface area of the shipping container:
Given that the container is a rectangular prism with dimensions 11 x 3 x 6:
Surface area of the container = 2lw + 2lh + 2wh
Surface area of the container = 2(11)(3) + 2(11)(6) + 2(3)(6)
Surface area of the container = 66 + 132 + 36 = 234 in^2
3. Surface area of the wheels (assuming they are cylinders):
Each wheel is a cylinder, and the formula for the surface area of a cylinder is 2πrh + πr^2, where r is the radius and h is the height (thickness) of the wheel.
Assuming the wheels have a radius of 2 inches and a width of 1 inch:
Surface area of each wheel = 2π(2)(1) + π(2)^2
Surface area of each wheel = 4π + 4π = 8π ≈ 25.13 in^2
Since there are 4 wheels on the truck, the total surface area of all 4 wheels is:
Total surface area of wheels = 4 * Surface area of each wheel
Total surface area of wheels = 4 * 8π ≈ 100.53 in^2
Now, add the surface areas of the cab, container, and the wheels together to get the total surface area of the truck:
Total surface area of the truck = Surface area of cab + Surface area of container + Total surface area of wheels
Total surface area of the truck = 75 + 234 + 100.53 ≈ 409.53 in^2
Therefore, the total surface area of the toy truck, including the wheels, is approximately 409.53 square inches.
1. Surface area of the cab:
Given that the cab has dimensions of 3 x 11 x 3:
Surface area of the cab = 2lw + lh
Surface area of the cab = 2(3)(11) + (3)(3)
Surface area of the cab = 66 + 9 = 75 in^2
2. Surface area of the shipping container:
Given that the container is a rectangular prism with dimensions 11 x 3 x 6:
Surface area of the container = 2lw + 2lh + 2wh
Surface area of the container = 2(11)(3) + 2(11)(6) + 2(3)(6)
Surface area of the container = 66 + 132 + 36 = 234 in^2
3. Surface area of the wheels (assuming they are cylinders):
Each wheel is a cylinder, and the formula for the surface area of a cylinder is 2πrh + πr^2, where r is the radius and h is the height (thickness) of the wheel.
Assuming the wheels have a radius of 2 inches and a width of 1 inch:
Surface area of each wheel = 2π(2)(1) + π(2)^2
Surface area of each wheel = 4π + 4π = 8π ≈ 25.13 in^2
Since there are 4 wheels on the truck, the total surface area of all 4 wheels is:
Total surface area of wheels = 4 * Surface area of each wheel
Total surface area of wheels = 4 * 8π ≈ 100.53 in^2
Now, add the surface areas of the cab, container, and the wheels together to get the total surface area of the truck:
Total surface area of the truck = Surface area of cab + Surface area of container + Total surface area of wheels
Total surface area of the truck = 75 + 234 + 100.53 ≈ 409.53 in^2
Therefore, the total surface area of the toy truck, including the wheels, is approximately 409.53 square inches.
11 answers