A cardboard box is open at one end and is shaped like a square prism missing one of its square bases. The volume of the prism is 810 cubic inches, and its height is 10 inches.
A)What is the length of each side of the base?
B)Draw a net of the box
C)How much cardboard is used for the box?
THANK YOU!!!!!
if the side of the base is s, then you know that
10s^2 = 810
The total area is the base (x^2) and 4 sides, each of area 10x.
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A) To find the length of each side of the base, we can use the formula for the volume of a square prism: Volume = length x width x height. In this case, we know the volume is 810 cubic inches and the height is 10 inches. Since one of the square bases is missing, the length and width of the base are the same. Let's call this unknown side length "x".
Thus, we have the equation: 810 = x * x * 10.
Simplifying this equation gives us: 810 = 10x^2.
Now, divide both sides of the equation by 10: 81 = x^2.
Next, take the square root of both sides to solve for x: √(81) = √(x^2).
This gives us two possible values for x: x = ±9.
Since a negative side length doesn't make sense in this context, we can conclude that the length of each side of the base is 9 inches.
B) To draw a net of the box, we need to visualize the unfolded shape of the box. Since the box is shaped like a square prism, it will have two square faces and four rectangular faces. One of the square bases is missing, so we will have three faces to show in the net. Here is a possible net of the box:
_________________
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|_____ _____|
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|_____|
In the above representation, the two square bases are shown at the top and bottom, and the missing square base is left open. The four rectangular faces connect the edges of the square bases.
C) To find out how much cardboard is used for the box, we need to calculate the total surface area of the box. Since the box is open at one end, we only need to consider the surface area of the sides and the one square base.
The surface area of a square prism is given by the formula: Surface area = 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height, respectively.
For the given box:
- The length of each side of the base (l) is 9 inches.
- The width (w) is also 9 inches, as it is the same as the length of each side of the base.
- The height (h) is 10 inches.
Now, substitute these values into the surface area formula:
Surface area = 2 * 9 * 9 + 2 * 9 * 10 + 2 * 9 * 10 = 162 + 180 + 180 = 522 square inches.
Therefore, the cardboard used to construct the box has a total surface area of 522 square inches.