To determine whether the $15 set aside for paint is enough to cover the entire surface area of the composite figure, we need to find out the total surface area of the figure in square feet and then divide that by the coverage area of a single can of paint (25 sq ft) to determine the number of cans required. Then we can multiply the number of cans by the cost per can ($6.79) to see if it exceeds the $15 budget.
Let's assume that the composite figure is made up of two shapes, a rectangular prism, and a triangular prism. The formula for finding the surface area of a rectangular prism is 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height of the prism respectively. The surface area of a triangular prism is given by the formula Ah + 2Bs, where A is the area of the base triangle, h is the height of the triangle, B is the base of the triangle, and s is the slant height of the triangular face.
Without specific measurements of the composite figure, we cannot calculate its exact surface area. Therefore, let's assume the surface area of the composite figure is 58 sq ft, as stated in the problem.
Let the surface area of the rectangular prism be x, and the surface area of the triangular prism be y. Then, we can write the equation:
x + y = 58
We can assume that the entire shape is to be painted silver, which means both the outer and inner surfaces of the two shapes.
For the rectangular prism, we have two pairs of identical faces, and for each pair, we need to paint both the outer and inner surfaces. Therefore, the surface area of the rectangular prism that needs to be painted is:
2(2lw + 2lh + 2wh) = 4lw + 4lh + 4wh
For the triangular prism, we have three faces that need to be painted - the two triangular faces and the rectangular face. We need to paint both the outer and inner surfaces of the triangular faces, and only the outer surface of the rectangular face. Therefore, the surface area of the triangular prism that needs to be painted is:
2(Ah + Bs) + Bw
where w is the width of the rectangular face.
Now we need to make some assumptions about the dimensions of the composite figure to proceed. Let's assume that the rectangular prism has a length of 3 ft, a width of 2 ft, and a height of 4 ft, and that the triangular prism has a base of 2 ft, a height of 4 ft, and a slant height of 5 ft.
Using these dimensions, we can calculate the surface areas of the rectangular and triangular prisms:
Surface area of rectangular prism = 4lw + 4lh + 4wh = 4(32 + 34 + 2*4) = 52 sq ft
Surface area of triangular prism = 2(Ah + Bs) + Bw = 2(1/224 + 25) + 22 = 24 sq ft
Total surface area of the composite figure = 52 + 24 = 76 sq ft
Now we can calculate the number of cans of paint required:
Number of cans = Total surface area / Coverage area of one can = 76 / 25 = 3.04 cans (rounded up to 4 cans)
The cost of 4 cans of paint is:
4 cans * $6.79 per can = $27.16
Since the cost of 4 cans of paint exceeds the set aside $15 for paint, it is