A box with a square base and no top is to be made from a square piece of carboard by cutting 6 in. squares
from each corner and folding up the sides. The box is to hold . How big a piece of cardboard is
needed?
Your answer is:

Question

A box with a square base and no top is to be made from a square piece of carboard by cutting 6 in. squares
from each corner and folding up the sides. The box is to hold

. How big a piece of cardboard is
needed?
Your answer is:

UpStudy AI · Accepted Answer

1. Let the side length of the original square piece of cardboard be $$ s $$. After cutting out a $$ 6 $$ in. square from each corner, the side length of the square base of the box becomes $$ s - 12 $$ (since $$ 6 $$ in. is removed from both ends).

2. The height of the box is $$ 6 $$ in. (equal to the side length of the cut-out squares).

3. The volume $$ V $$ of the open-top box is given by
   $$
   V = 6\,(s-12)^2.
   $$
   Since the box must hold $$ 5046 $$ in.$$^3$$, we have
   $$
   6\,(s-12)^2 = 5046.
   $$

4. Divide both sides of the equation by $$ 6 $$:
   $$
   (s-12)^2 = \frac{5046}{6} = 841.
   $$

5. Taking the square root of both sides (and retaining the positive root, since $$ s $$ represents a length):
   $$
   s - 12 = \sqrt{841} = 29.
   $$

6. Solve for $$ s $$:
   $$
   s = 29 + 12 = 41.
   $$

7. Therefore, the piece of cardboard must be a square of side length $$ 41 $$ in. Its area is
   $$
   41^2 = 1681 \; \text{in}^2.
   $$

Thus, the required piece of cardboard is $$ 41 $$ in. by $$ 41 $$ in., with an area of $$ 1681 $$ in.$$^2$$.
A square piece of cardboard with sides of 41 inches is needed, which has an area of 1681 square inches.

A box with a square base and no top is to be made from a square piece of carboard by cutting 6 in. squares
from each corner and folding up the sides. The box is to hold . How big a piece of cardboard is
needed?
Your answer is:

Upstudy AI Solution

Answer

Solution

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Latest Geometry Questions

A box with a square base and no top is to be made from a square piece of carboard by cutting 6 in. squares from each corner and folding up the sides. The box is to hold . How big a piece of cardboard is needed? Your answer is:

Upstudy AI Solution

Answer

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Latest Geometry Questions

A box with a square base and no top is to be made from a square piece of carboard by cutting 6 in. squares
from each corner and folding up the sides. The box is to hold . How big a piece of cardboard is
needed?
Your answer is: