Solve the surface area of the letter C 15 ft high, 15ft high,4 ft wide?
The surface area of the letter C can be broken down into three parts: the top half circle, the bottom half circle, and the rectangular connecting piece.
The top and bottom half circles have the same dimensions, so we can calculate the surface area of one and double the result. The formula for the surface area of a half sphere is:
SA = 2πr^2
where r is the radius of the half sphere. Since the letter C is 15 ft high, we know that the radius is half of the height or 7.5 ft.
SA half sphere = 2π(7.5)^2 ≈ 353.43 ft^2
Doubling this result, we get:
SA top and bottom half circles = 2(353.43) ≈ 706.86 ft^2
Now we need to find the surface area of the rectangular connecting piece. The formula for the surface area of a rectangular prism is:
SA = 2lw + 2lh + 2wh
where l, w, and h are the length, width, and height of the prism. Since the letter C is 4 ft wide and 15 ft high, we know that one side of the rectangular connecting piece is 4 ft wide and 15 ft high. The length of the piece is the circumference of a circle with a radius of 7.5 ft (the same as the half spheres). The formula for circumference is:
C = 2πr
where r is the radius. Plugging in 7.5 ft for r, we get:
C = 2π(7.5) ≈ 47.12 ft
So the length of the rectangular connecting piece is approximately 47.12 ft. Plugging in the dimensions, we get:
SA rectangular piece = 2(4)(15) + 2(4)(47.12) + 2(15)(47.12) ≈ 1691.84 ft^2
Adding the surface areas of the top and bottom half circles and the rectangular connecting piece, we get the total surface area of the letter C:
SA C = 706.86 + 1691.84 ≈ 2398.7 ft^2
Therefore, the surface area of the letter C is approximately 2398.7 square feet.