To find the surface area of the letter C, we first need to find the surface area of each individual part.
1. Top and bottom arms:
- The top and bottom arms are rectangular prisms with dimensions 10 feet wide, 1 foot deep, and 4 feet high each.
- The surface area of one arm = 2(10 x 1) + 2(10 x 4) + 2(1 x 4) = 2(10) + 2(40) + 2(4) = 20 + 80 + 8 = 108 ft²
- Total surface area of both arms = 2(108) = 216 ft²
2. Remaining part:
- The remaining part is a rectangular prism with dimensions 7 feet wide, 1 foot deep, and 15 feet high.
- The surface area of the remaining part = 2(7 x 1) + 2(7 x 15) + 2(1 x 15) = 2(7) + 2(105) + 2(15) = 14 + 210 + 30 = 254 ft²
Therefore, the total surface area of the letter C sculpture is:
Total surface area = Surface area of top and bottom arms + Surface area of remaining part
Total surface area = 216 ft² + 254 ft² = 470 ft²
So, the surface area of the letter C sculpture is 470 ft².
Surface Area Unit Test
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?
(1 point)
ft.2
1 answer