A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in squares from each corner and folding up the sides... the box is told 100 in cube, how big a piece of cardboard is needed?
If you mean "The box has a total volume of 100 in^3, then
(1) The sides of the box are 4 in high, so the base area must be 25 in^2
(2) That means the box sides are 5 inches long
(3) The original cardboard square piece must be 5 + 4 + 4 = 13 inches on a side, so that you will have a 5-inch-square base when the 4-inch-square corners are cut off
A rectangle is 20 inches tall it's area is 260 inches what is the width
To find out the size of the piece of cardboard needed to create the box, we need to determine the dimensions of the square base.
Let's assume the sides of the square base have a length of x inches.
Since 4-inch squares are cut from each corner of the cardboard, the resulting box will have dimensions of (x-8) inches by (x-8) inches by 4 inches (height).
To find the volume of the box, we multiply the three dimensions:
Volume = (x-8) * (x-8) * 4
We know that the volume of the box is 100 cubic inches, so we can set up the equation:
100 = (x-8) * (x-8) * 4
Simplifying:
25 = (x-8)^2
Taking the square root of both sides:
±5 = x-8
Ignoring the negative solution, we have:
5 = x - 8
Solving for x:
x = 5 + 8
x = 13
The length of each side of the square base is 13 inches.
To find the dimensions of the cardboard piece needed, we add the 4-inch squares that were cut from each corner to the length of the base:
Length of cardboard = x + 2 * 4
Length of cardboard = 13 + 2 * 4
Length of cardboard = 13 + 8
Length of cardboard = 21
Therefore, a piece of cardboard measuring 21 inches by 21 inches is needed to create the box.
To determine how big a piece of cardboard is needed to make the box, we need to follow these steps:
1. Start by visualizing the given box with a square base and no top.
2. Since we are cutting 4-inch squares from each corner, this means the length and width of the base of the box will be reduced by 8 inches (2 squares from each side).
3. Let's say the side length of the square cardboard initially is "x".
4. After cutting 4-inch squares from each corner, the new base dimensions will be (x - 8) inches.
5. Folding up the sides of the cardboard will create a box with a height of 4 inches.
6. Since the box is a cube with a volume of 100 cubic inches, the volume can be calculated as (length of base) * (width of base) * (height).
So, (x - 8) * (x - 8) * 4 = 100.
7. Simplifying the equation, we get (x^2 - 16x + 64) * 4 = 100.
8. Expanding the equation further, we have 4x^2 - 64x + 256 = 100.
9. Rearranging the equation to form a quadratic equation in standard form, we get 4x^2 - 64x + 156 = 0.
10. To solve the quadratic equation, we can use factoring, completing the square, or the quadratic formula. In this case, the quadratic equation can be factored as (2x - 13)(2x - 12) = 0.
11. Setting each factor equal to zero, we can find the possible values of 'x': 2x - 13 = 0 or 2x - 12 = 0.
12. Solving these equations, we find x = 13/2 or x = 6.
13. Since the dimensions of a square cannot be negative, we discard the solution x = 13/2.
14. Therefore, the side length of the square cardboard needed to construct the box is 6 inches.
15. To find the total area of cardboard needed, we calculate the area of the square cardboard: x * x = 6 * 6 = 36 square inches.
16. Hence, a square piece of cardboard with dimensions 6 inches by 6 inches is needed to construct the box.