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?
To find the surface area of the 3-dimensional vertical rectangular prism that appears as the letter upper C, we first need to find the surface area of each individual component and then sum them up.
1. Top and Bottom surfaces:
Each arm has dimensions of 15 feet by 4 feet, so the surface area of one arm is:
15 feet * 4 feet = 60 square feet
Since there are 2 arms (top and bottom), the total surface area of the top and bottom surfaces is:
2 * 60 square feet = 120 square feet
2. Front and Back surfaces:
The front and back surfaces have dimensions of 15 feet by 10 feet, so the surface area of each arm is:
15 feet * 10 feet = 150 square feet
Since there is 1 front and 1 back surface, the total surface area of the front and back surfaces is:
2 * 150 square feet = 300 square feet
3. Side surfaces:
The side arm that was removed has dimensions of 1 foot by 7 feet, so the surface area of this arm is:
1 foot * 7 feet = 7 square feet
Since there is 1 side arm, the total surface area of the side surface is:
1 * 7 square feet = 7 square feet
Now, we sum up all the surface areas to find the total surface area of the letter C sculpture:
120 square feet (top and bottom) + 300 square feet (front and back) + 7 square feet (side) = 427 square feet
Therefore, the surface area of the letter C sculpture is 427 square feet.