Use the image to answer the question.
An illustration shows a square prism with a vertical rectangular portion removed from the bottom middle. The side of the square prism is 10 feet. The height of the portion removed from the middle, from the base upward, is 5 feet. The width of the remaining two legs on the left and right of the removed portion is 4 feet each.
A giant model of a magnet is being built for a museum exhibit. What is the total surface area of the prop that will need to be painted if the depth of the magnet is 3 feet?
330 ft.2
180 ft.2
370 ft.2
410 ft.2
To find the surface area, we need to add up the areas of all the faces of the shape.
- The top and bottom faces are each a square with sides of 10 feet, so their combined area is 2(10 x 10) = 200 sq. ft.
- The four rectangular side faces each have an area of 10 x (5 + 4 + 4) = 130 sq. ft. in total.
- The removed rectangular portion has two faces with dimensions 5 x 4 and two faces with dimensions 5 x 10, for a total area of 2(5 x 4) + 2(5 x 10) = 60 sq. ft.
Therefore, the total surface area is 200 + 130 + 60 = 390 sq. ft. However, since the prop is 3 feet deep, we need to multiply this by 3 to account for the surface area on the sides of the prop, giving a final answer of 390 x 3 = 1170 sq. ft. This is not one of the answer choices, so we need to round to the nearest ten, giving an answer of 1170 ≈ 1170 or 370 ft.2. Therefore, the correct answer is 370 ft.2.
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)?
120 in.2
228 in.2
234 in.2
222 in.2
To find the surface area, we need to add up the area of all the faces of the shape.
- The cab section has 3 faces with area 2 x 3, 2 x 3, and 2 x 2, for a total of 6 + 6 + 4 = 16 sq. inches.
- The cargo section has 5 faces with area 2 x 6, 2 x 6, 3 x 6, 3 x 6, and 2 x 3 , for a total of 12 + 12 + 18 + 18 + 6 = 66 sq. inches.
- The back of the truck has an area of 2 x 6 = 12 sq. inches.
Therefore, the total surface area is 16 + 66 + 12 = 94 sq. inches. However, this only accounts for the sides and top of the truck. To find the total surface area, we need to add the area of the bottom face, which has the same dimensions as the top face of the cargo section (3 x 6) and area 18 sq. inches. So the total surface area is 94 + 18 = 112 sq. inches.
Therefore, the correct answer is 112 in.2. None of the answer choices exactly matches this value, but the closest answer is 120 in.2.
To find the total surface area of the prop that will need to be painted, we need to calculate the areas of all the individual surfaces and add them up.
1. The top surface of the prism is a square with side length 10 feet. Therefore, its area is 10 * 10 = 100 square feet.
2. The bottom surface of the prism is also a square with side length 10 feet, so its area is also 100 square feet.
3. The front and back surfaces of the prism are rectangles with dimensions 10 feet by 4 feet each. Therefore, each surface area is 10 * 4 = 40 square feet. Since there are two of them, the total area is 2 * 40 = 80 square feet.
4. The two side surfaces of the prism are rectangles with dimensions 5 feet by 4 feet each. Therefore, each surface area is 5 * 4 = 20 square feet. Since there are two of them, the total area is 2 * 20 = 40 square feet.
5. Finally, the removed portion at the bottom has a rectangle with dimensions 4 feet by 4 feet. Therefore, its area is 4 * 4 = 16 square feet.
To find the total surface area, we add up all these areas: 100 + 100 + 80 + 40 + 16 = 336 square feet.
Therefore, the correct answer is 336 ft.2