Santana wants to cover a gift box shaped like a rectangular prism with foil. The foil costs $0.03 per square inch. Santana has a choice between Box A which is 8 inches long, 3 inches wide, and 6 inches high, and Box B which is 10 inches long, 3 inches wide, and 4 inches high. Which box will be less expensive to cover with foil, and by how much?

THANKS!!!!!

Box A:

2(8x3) + 2(8x6) + 2(3x6)
2(24) + 2(48) + 2(18)
48 + 96 + 36 = 180in2

Box B:
2(10x3) + 2(10x4) + 2(3x4)
2(30) + 2(40) + 2(12)
60 + 80 + 24 = 164in2

Box A: 180 x 0.03 = 5.40
Box B: 164 x 0.03 = 4.92
5.40 - 4.92 = $0.48

Answer: Box B - $0.48

2(8 * 3) + 2(8 * 6) + 2(3 * 6) = _____ sq. in

Do the same for Box B.

Box b by .48

Yes thanks

thanks dude

To determine which box will be less expensive to cover with foil and by how much, we need to calculate the surface area of each box and then multiply it by the cost per square inch of the foil.

1. Calculate the surface area of Box A:
The surface area of a rectangular prism is given by the formula:
2lw + 2lh + 2wh

For Box A:
Length (l) = 8 inches
Width (w) = 3 inches
Height (h) = 6 inches

Surface Area of Box A = 2(8*3) + 2(8*6) + 2(3*6)
Surface Area of Box A = 48 + 96 + 36
Surface Area of Box A = 180 square inches

2. Calculate the surface area of Box B:
Using the same formula as above, but applying the dimensions of Box B:
Length (l) = 10 inches
Width (w) = 3 inches
Height (h) = 4 inches

Surface Area of Box B = 2(10*3) + 2(10*4) + 2(3*4)
Surface Area of Box B = 60 + 80 + 24
Surface Area of Box B = 164 square inches

3. Calculate the cost for covering each box with foil:
Cost of foil per square inch = $0.03

Cost of covering Box A = Surface Area of Box A * Cost of foil per square inch
Cost of covering Box A = 180 * $0.03
Cost of covering Box A = $5.40

Cost of covering Box B = Surface Area of Box B * Cost of foil per square inch
Cost of covering Box B = 164 * $0.03
Cost of covering Box B = $4.92

Thus, Box B will be less expensive to cover with foil, by $5.40 - $4.92 = $0.48.