Surface Area Unit Test

Question

14 of 1514 of 15 Items

Question
Use the image to answer the question.

An illustration shows a 3-dimensional vertical rectangular prism that appears as the letter upper C, with a rectangular portion removed from the right center. The rectangular prism is 15 feet high, 10 feet wide, and 1 foot deep. The width of the portion removed from the middle on the right side is 7 feet across. The height of the remaining two arms left at the top and bottom is 4 feet each.

In Los Cabos, Mexico, there is a big sculpture of block letters that welcomes you. The image shows the letter C . What is its surface area?

Answer 1

To find the surface area of the letter C sculpture, we need to calculate the surface area of each individual face and then add them up.

The total surface area of a rectangular prism can be calculated using the formula: 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.

1. The front face (15 ft x 10 ft) = 150 sq.ft
2. The back face (15 ft x 10 ft) = 150 sq.ft
3. The top and bottom faces (10 ft x 1 ft) = 10 sq.ft each (since there are two)
4. The left side face (15 ft x 1 ft) = 15 sq.ft
5. The right side face consists of two portions:
- portion 1 = (15 ft x 7 ft) = 105 sq.ft
- portion 2 = (15 ft x 3 ft) = 45 sq.ft

Adding all these up:
Total surface area = 150 + 150 + 10 + 10 + 15 + 105 + 45 = 485 sq.ft

Therefore, the surface area of the letter C sculpture is 485 square feet.

Answer 2

wrong

Answer 3

I apologize for the mistake. Let's recalculate the surface area of the letter C sculpture:

1. Front Face: 15 ft * 10 ft = 150 sq.ft
2. Back Face: 15 ft * 10 ft = 150 sq.ft
3. Left Side Face: 15 ft * 1 ft = 15 sq.ft
4. Right Side Face (with cutout):
Remaining portion = 15 ft * (10 ft - 7 ft) = 15 ft * 3 ft = 45 sq.ft
Cutout portion = 15 ft * 7 ft = 105 sq.ft
Total Right Side Face: 105 sq.ft - 45 sq.ft = 60 sq.ft
5. Top Face: 7 ft * 1 ft = 7 sq.ft
6. Bottom Face: 7 ft * 1 ft = 7 sq.ft

Now, calculate the total surface area by adding up all these individual face areas:
Total Surface Area = 150 sq.ft (Front) + 150 sq.ft (Back) + 15 sq.ft (Left) + 60 sq.ft (Right) + 7 sq.ft (Top) + 7 sq.ft (Bottom)
Total Surface Area = 150 + 150 + 15 + 60 + 7 + 7
Total Surface Area = 389 sq.ft

Therefore, the correct surface area of the letter C sculpture is 389 square feet.

Answer 4

still wrong

Answer 5

I apologize for the errors in my previous calculations. Let's try again:

1. Front face: 15 ft * 10 ft = 150 sq.ft
2. Back face: 15 ft * 10 ft = 150 sq.ft
3. Top face (portion above the cutout): 4 ft * 10 ft = 40 sq.ft
4. Bottom face (portion below the cutout): 4 ft * 10 ft = 40 sq.ft
5. Left side face: 15 ft * 1 ft = 15 sq.ft
6. Right side face (remaining portion): 15 ft * (10 ft - 7 ft) = 15 ft * 3 ft = 45 sq.ft
7. Right side face (cutout portion): 15 ft * 7 ft = 105 sq.ft

Add up all these individual face areas now:
Total Surface Area = 150 sq.ft (Front) + 150 sq.ft (Back) + 40 sq.ft (Top) + 40 sq.ft (Bottom) + 15 sq.ft (Left) + 45 sq.ft (Right - remaining portion) + 105 sq.ft (Right - cutout portion)
Total Surface Area = 150 + 150 + 40 + 40 + 15 + 45 + 105
Total Surface Area = 545 sq.ft

Therefore, the correct surface area of the letter C sculpture is 545 square feet.

Answer 6

i think it is 170

Answer 7

Let's reevaluate the calculation:

The total surface area can be calculated by adding the areas of each face of the 3-dimensional vertical rectangular prism.

1. Front face: 15 ft (height) * 10 ft (width) = 150 sq.ft
2. Back face: 15 ft * 10 ft = 150 sq.ft
3. Top face (above the cutout): 4 ft * 10 ft = 40 sq.ft
4. Bottom face (below the cutout): 4 ft * 10 ft = 40 sq.ft
5. Left side face: 15 ft (height) * 1 ft (depth) = 15 sq.ft
6. Right side face (remaining portion): 15 ft * 3 ft = 45 sq.ft

Now, sum up these individual face areas:
Total Surface Area = 150 sq.ft (Front) + 150 sq.ft (Back) + 40 sq.ft (Top) + 40 sq.ft (Bottom) + 15 sq.ft (Left) + 45 sq.ft (Remaining right side)
Total Surface Area = 150 + 150 + 40 + 40 + 15 + 45
Total Surface Area = 440 sq.ft

Therefore, the correct surface area of the letter C sculpture is 440 square feet, not 170 square feet. Thank you for your patience.