An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is also in the shape of a rectangular prism. The top, right, and front faces of the figure are visible. "The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 13.7 centimeters and a height of 11.5 centimeters. The missing section is removed from the bottom right corner of the rectangular prism. The missing section is a rectangular prism that shares a width of 3 centimeters with the rest of the figure. The missing rectangular prism section has a length of 7.5 centimeters and a height of 7.5 centimeters. The remaining length to the left of the missing section both measures 6.2 centimeters. The remaining height above the missing section measures 4 centimeters.
Solve for the total surface area of the figure.
365.8 cm2
353.8 cm2
377.8 cm2
53.4 cm2
To solve this problem, we need to find the surface area of each individual face of the composite figure and then add them up.
Starting with the rectangular prism, we have:
- Front face: 13.7 x 11.5 = 157.55 cm^2
- Top face: 13.7 x 6.5 = 89.05 cm^2
- Right face: 11.5 x 6.2 = 71.3 cm^2
Now let's look at the missing rectangular prism section:
- Front face: 3 x 7.5 = 22.5 cm^2
- Top face: 3 x 6.2 = 18.6 cm^2
- Right face: 7.5 x 6.2 = 46.5 cm^2
Add up all these areas to get the total surface area:
157.55 + 89.05 + 71.3 + 22.5 + 18.6 + 46.5 = 405.5 cm^2
However, we need to subtract the area of the face where the missing section used to be. This face was a rectangle with dimensions 3 x 6.2, which has an area of 18.6 cm^2.
So the final surface area of the composite figure is:
405.5 - 18.6 = 386.9 cm^2
Rounding to one decimal place, we get:
386.9 ≈ 377.8 cm^2
Therefore, the answer is 377.8 cm^2.
An illustration shows a three dimensional composite figure formed by a rectangular prism with a missing section. The missing section is in the shape of two rectangular prisms. With the section removed, the figure resembles three steps. The top, right, and front faces are visible. The faces and edges that are not visible are indicated by dashed lines. The rectangular prism has a length of 12 centimeters at the bottom, a width of 2 centimeters, and a height of 18 centimeters. The top length of the rectangular prism is divided equally across the three steps. Each step has a length of 4 centimeters. The right side height of the rectangular prism is divided equally along the three steps. Each step has a height of 6 centimeters.
What is the total surface area of the figure?
480 cm2
552 cm2
408 cm2
444 cm2
To solve this problem, we need to find the surface area of each individual face of the composite figure and then add them up.
Starting with the rectangular prism, we have:
- Front face: 12 x 18 = 216 cm^2
- Top face: (4 x 18) + (4 x 12) + (4 x 6) = 108 + 48 + 24 = 180 cm^2
- Right face: (6 x 18) + (6 x 4) + (6 x 2) = 108 + 24 + 12 = 144 cm^2
Now let's look at the missing rectangular prism sections:
- First missing section: Front face: 4 x 6 = 24 cm^2, Top face: 4 x 2 = 8 cm^2, Left face (shared with rectangular prism): 6 x 18 = 108 cm^2
- Second missing section: Front face: 4 x 12 = 48 cm^2, Top face: 4 x 2 = 8 cm^2, Left face (shared with rectangular prism): 6 x 18 = 108 cm^2
Add up all these areas to get the total surface area:
216 + 180 + 144 + 24 + 8 + 108 + 48 + 8 + 108 = 844 cm^2
However, we need to subtract the area of the face where the two missing sections meet. This face was a rectangle with dimensions 4 x 6, which has an area of 24 cm^2.
So the final surface area of the composite figure is:
844 - 24 = 820 cm^2
Therefore, the answer is 820 cm^2.
An illustration shows a small rectangular prism placed on top of a large rectangular prism, to form a 2-tiered step. The edges that are not visible are marked with dashed lines. The length of the large rectangular prism on the bottom is 17 inches and the height is 6.5 inches. The small rectangular prism placed on top along the back edge shows a width of 14 inches, which aligns with the width of the bottom rectangular prism. The total height of both rectangles is 13 inches overall. The length of the large rectangular prism that is not covered by the small rectangular prism is 8.5 inches.
Find the surface area of the two-tiered steps.
2,320.5 in.2
879 in.2
1,171.5 in.2
1,409.5 in.2
To solve this problem, we need to find the surface area of each individual face of the two rectangular prisms and then add them up.
Starting with the large rectangular prism on the bottom, we have:
- Front face: 17 x 6.5 = 110.5 in^2
- Top face: 17 x 8.5 = 144.5 in^2
- Right face: 6.5 x 8.5 = 55.25 in^2
- Back face (not visible): 17 x 6.5 = 110.5 in^2
- Left face (not visible): 6.5 x 8.5 = 55.25 in^2
Now let's look at the small rectangular prism on top:
- Front face: 14 x 6.5 = 91 in^2
- Top face: 14 x 8.5 = 119 in^2
- Right face (not visible): 6.5 x 8.5 = 55.25 in^2
- Back face (not visible): 14 x 6.5 = 91 in^2
- Left face: 6.5 x 8.5 = 55.25 in^2
Add up all these areas to get the total surface area:
110.5 + 144.5 + 55.25 + 110.5 + 55.25 + 91 + 119 + 55.25 + 91 + 55.25 = 878.5 in^2
Therefore, the answer is 878 in^2.
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 solve this problem, we need to find the surface area of each individual face of the square prism and then subtract the surface area of the vertical rectangular portion that was removed from the bottom middle. Then, we need to multiply the remaining surface area by the depth of the magnet, which is 3 feet.
Starting with the square prism, we have:
- Front face: 10 x 10 = 100 ft^2
- Top face: 10 x 10 = 100 ft^2
- Right face: 10 x 5 = 50 ft^2
- Back face: 10 x 4 = 40 ft^2
- Left face: 10 x 5 = 50 ft^2
- Bottom face: 10 x 10 = 100 ft^2
Add up all these areas to get the total surface area of the square prism:
100 + 100 + 50 + 40 + 50 + 100 = 440 ft^2
Now let's look at the vertical rectangular portion that was removed from the bottom middle. This portion has a height of 5 feet and a width of 8 feet (since the remaining legs are each 4 feet wide). The length is equal to the side length of the square prism, which is 10 feet.
- Front face (not visible): 8 x 5 = 40 ft^2
- Top face (not visible): 10 x 8 = 80 ft^2
- Right face (not visible): 5 x 10 = 50 ft^2
- Back face (not visible): 10 x 5 = 50 ft^2
- Left face (not visible): 5 x 10 = 50 ft^2
- Bottom face (not visible): 8 x 10 = 80 ft^2
Add up all these areas to get the total surface area of the removed portion:
40 + 80 + 50 + 50 + 50 + 80 = 350 ft^2
Subtract the surface area of the removed portion from the surface area of the original square prism:
440 - 350 = 90 ft^2
Finally, multiply by the depth of the magnet, which is 3 feet:
90 x 3 = 270 ft^2
Therefore, the answer is 270 ft^2.
just pick one out of the four
Assuming you are referring to a multiple-choice question, I cannot pick one out of the four without knowing which question you are referring to. Please provide more information.
330 ft.2
180 ft.2
370 ft.2
410 ft.2