SOLUTION: An open-topped box is constructed froma square piece of cardboard by removing a square of size 5 inches from each corner and turning up the edges. If the box is to hold 9,680 i

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Question 1196695: An open-topped box is constructed froma square piece of cardboard by removing a square of size 5 inches from each corner and turning up the edges.
If the box is to hold 9,680 in3, how big should the originial piece of cardboard be?

Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

The volume will be
V=+L%2AW%2AH
We are cutting 5 inches from each corner, so the length and width will each be
x+-+10.
The height will be 5in.
if V=+9680in%5E3+, then
9680in%5E3++=+5in%2A+%28x+-+10in%29%2A+%28x+-+10in%29
9680in%5E3++=+5in%2A+%28x+-+10in%29%5E2
9680in%5E3%2F+5in=+%28x+-+10in%29%5E2
1936in%5E2=+%28x+-+10in%29%5E2........take square root of both sides
44in=x+-+10in
44in%2B10in=x+
x=54in

The piece of cardboard needed will be 54 by 54 inches.


Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the length of a side of the box; then the volume 9680 is 5x^2.

5x^2 = 9680
x^2 = 9680/5 = 1936
x = sqrt(1936) = 44

Since 5 inches were cut out of each corner of the original piece of cardboard, the side length of the original piece of cardboard was 44+2(5) = 54 inches.

ANSWER: 54 inches