SOLUTION: 1) A box with a square base and no top is to be made from a square piece of tin by cutting out 3-inch squares from each corner and folding up the sides. If the box is to hold 48 cu

Question 471145: 1) A box with a square base and no top is to be made from a square piece of tin by cutting out 3-inch squares from each corner and folding up the sides. If the box is to hold 48 cu. in., what size of tin should be used?
2) Orlando won $200.000 in a state lottery. He first paid an income tax of 30% of the winnings and the rest he invested at 8.5% and 7% earning $10,700 interest a year. How much did he invest at each rate?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
box has a square base.
box has no top.
piece of tin is square (assumed).
box needs to hold 48 cubic inches.
formula for volume of this box is L*W*H = 48
Since L = W, then the formula for the volume of this box becomes:
S^2*H = 48
We simply just made L = S and W = S and substituted in the volume equation.
The equation for the volume of the box is S^2*H = 48
Since we cut 3 inch squares from each corner of the box, then the height of our box will be 3 inches.
Substitute this in our equation for the box and we get:
S^2*3 = 48
divide both sides of this equation by 3 to get:
S^2 = 48/3 = 16
take the square root of each side of this equation to get:
S = 4
Our box will be 4 inches long by 4 inches wide by 3 inches high.
The volume of our box will be 4*4*3 = 48 cubic inches.
The bottom of the box is square (L = 4 and W = 4)
It is assumed that the dimensions of the original piece of tin was:
L = 4 + 6 = 10
W = 4 + 6 = 10
That means that the area of the original piece of tin was 100 square inches.
We removed 3 inch squares from each corner which means we removed 9*4 = 36 square inches from the area of the original piece of tin.
This left 100 - 36 = 64 square inches of tin that was used to make the open ended box.
The surface area of the tin box is equal to the area of the bottom plus 4 times the area of each side.
The area of the bottom is 4*4 = 16 square inches.
The area of each side is equal to 4*3 = 12 square inches.
16 square inches + 4*12 square inches = 16 + 48 = 64 square inches.
That's exactly what it should be, so we're good all around.

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