You have to make a square-bottomed, box (without a lid,) with a height of three inches and a volume of approximately 42 cubic inches. You will be taking a piece of cardboard, cutting three-inch squares from each corner, scoring between the corners, and folding up the edges. What should be the dimensions of the cardboard, to the nearest quarter inch?
Credit: Elizabeth Stapal
Be sure to include an explaination of how you solved this and an equation that would be helpful in solving this problem. Then solve the equation to prove your answer. Be sure to include all the steps in your solution with the equation. We should never have to guess what you did or feel like there is a step missing for either your process or your equation.
DC
ReplyDeleteThe data I am given is that the volume is 42 in3 and the height of the box is 3 in. I can find the base of the box by dividing 42, the volume, by 3, the height. 42 divided by 3 is 14 in2, the base. Now that I know the base I can find the dimensions of it. It is a square so you can find its square root and find the base’s dimensions. √14 is equal to 3.741 in so this is the number for both of the sides. Now you have to add three to each side (a total of four 3’s) I have to add 6 to each 3.741 to get 9.741 in. The dimensions of the cardboard should be 9.741 in X 9.741 in.
L.A.
ReplyDeleteV = b * h * w
42 = b * 3 * w
42 / 3 = 14
Factors of 14: 7 & 2
3 * 2 * 7 = 42
Height: 3
Base: 7
Width: 2
If you work backwards from the volume equation of a prism (in this case, a box…), you would end up with the only answer possible from the given height of 3; 7 and 2. (See problem above)
AC
ReplyDeleteVolume of box = 42 In3
42/ 3= 14
Base = 14 In2
Square root of 14= 3.742
1 side of base = 3.742 inches
3.742+ 3+ 3= 9.742
To get my answer of 9.742 I started with the volume of the box. I knew that since the height was 3 that I could divide 42 by 3 to get the area of the base. This was 14 in2. Since the base was still in area and not length form I found the square root of 14, since the box was a square. This meant that each side of the base was 3.742 in. To finish the problem I added 3 in. on to each side so I would have found the length of all four sides of the whole folded out square.
AC Work
ReplyDelete42 = Volume
6 x 7 = 42
3 x 2 x 7= 42
One layer = 14 square inches
7 x 2 = 14
13 x 13 = Width and Length
This is because the square without the four sides will be three layers of 14 (3.74 x 3.74)
I got that answer because since it is a square the sides would be the same width and length, and since 14 x 3 is 42, I used that to find the square root of 14, which rounded, is around 3.74.
Square = Even sides
3.74 x 3.74 = ~14
14 x 3 = 42
P.H
ReplyDeleteThe dimensions of the inner square (the base) need to be 9.74. I got this by dividing 42 (the volume) by 3 (the height). This gave me the answer 14. I then found the square root of 14 (length times width) and the answer came to be 3.74. Then I added 6 to each of the sides (because the height on each side and you combine two sides). Then the answer came out to be 9.74.
S.A.
ReplyDeleteVolume of box=42 in.3
42/3=14
Base: 14
Square root of 14=3.742
3.742 +3+3=9.742
Width= 9.742
I took the volume of the box which was 42 inches cubed and divided it by 3 to get the base. Then I found the square root of 14 to get the side length of the base which was 3.742. I added 6 to it to find the width of the box, my final answer was 9.742.
G.F.
ReplyDeleteFirst off, I remembered the equation for volume: l*w*h or base*height. The height is 3 inches and I figured out the base of the box by dividing 42 by 3:14 inches squared. Next, I found the square root of 14: 3.74-this will be be the length and width of the cube. To check my answer, I multiplied 3.74*3.74*3, which equals approximately 42 inches cubed.
If V = L x H x W, then in this problem 42 = 3 x X x X or 42 = 3 x X^2.
ReplyDelete42/3 = X^2
14 = X^2
√14 = 3.74
3.74 = X
H = 3
W = 3.74
L = 3.74
The four excess squares on the figure that will be cut have the dimensions of 3’’ by 3’’.
To find the dimensions of the whole square cut we add 3+3 to put together the 2 lengths of the excess boxes and 3.75, for the part not cut.
3 + 3 = 6
6 + 3.74 = 9.74
The whole square cut has the dimensions of 9.74’’ by 9.74’’.
LW
TK
ReplyDeleteThe volume of the square box is 423 inches. The height of the box is three inches. Therefore, since the equation for Volume is LengthxWidthxHeight, you are able to divide 42 (volume) by 3 (dimensions) to get the base of the square. 42/3=14. Then, you would need to find the square root of 14 to get each dimension of the base. The square root of 14 is about 3.74, but you can’t forget the three on each corner. So, since there is a 3 on each side of the square, you would add 3.74 + 6= 9.74 twice. To conclude, each dimension of the base would equal 9.74 inches.
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ReplyDelete