Raymond wants to make a box that has a volume of 360 cubic inches. He wants the height to be 10 in. and the other dimensions to be whole numbers of inches. how many different sized boxes can he make?
Let's cal the two unknown dimensions n and m, then 10nm=360 hence n*m=36
36=3*3*2*2 hence there are 5 ways to choose the dimensions.
Volume=L×w×h=360
L×w×10=360
L×w=36/10
L×w=36
You would have to find all the possible factors of 36
We include
1,2,3,4,6,9,12,18,36
L×w=36×1
L×w=9×4
L×w=18×2
If the L=36 ,w=1 & h=10
L×w×h=36×10×1=360✓
So what possible combination can you see? knowing that when multiplied gives you 36... If the L>w
??
Discovered a typo
L×w×10=360
L×w=360/10=36
But nothing changes just and error
To find the different sized boxes that Raymond can make, we need to determine the possible values for the length and width of the box.
Since the volume of the box is given as 360 cubic inches, we can express it using the formula:
Volume = Length * Width * Height
Since the height is fixed at 10 inches, we have:
360 = Length * Width * 10
To find the different possible sizes, we can start by finding the factors of 360. A factor is a number that evenly divides the given number without leaving a remainder.
The factors of 360 are: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.
Now, we need to pair up the factors to find the possible lengths and widths of the boxes. Since Raymond wants whole numbers of inches, the length and width must pair up to give a whole number when divided by 10.
For example:
- If the length is 6 and the width is 60, the volume would be 6 * 60 * 10 = 360. This is a valid combination.
- If the length is 2 and the width is 40, the volume would be 2 * 40 * 10 = 800. This is not a valid combination because it doesn't give the desired volume of 360.
By going through each factor, pairing up the appropriate lengths and widths, and checking if the volume is 360, we can determine how many different sized boxes Raymond can make.