To find the volume of a box, you can multiply its height, length, and width. The measure of the volume of a box is 357. Find its possible dimensions.
357 = 3x7x17 in prime factored form
So if you want the dimensions to be whole numbers, then those are the only possible dimensions.
If you allow fractions or decimals, there would be infinite number of possiblities.
e.g. (3/5)(35/2)(34) , but notice we end up with 3x7x17
To find the possible dimensions of the box, we will need to find the factors of the volume, which is 357. This can be done by dividing 357 by different numbers and checking if the division is exact, without any remainder. Let's go step by step.
We start by dividing 357 by 2:
357 ÷ 2 = 178.5 (not exact, with decimal)
Next, we divide 357 by 3:
357 ÷ 3 = 119 (not exact, without decimal)
Now, we divide 357 by 4:
357 ÷ 4 = 89.25 (not exact, with decimal)
Continuing, we divide 357 by 5:
357 ÷ 5 = 71.4 (not exact, with decimal)
Next, we divide 357 by 6:
357 ÷ 6 = 59.5 (not exact, with decimal)
Dividing 357 by 7:
357 ÷ 7 = 51 (exact)
Since 357 divided by 7 is an exact division, 7 is one of the possible dimensions of the box.
Next, we can find another dimension by dividing 357 by 7:
357 ÷ 7 = 51 (exact)
Therefore, the possible dimensions of the box are:
Height: 7 units
Length: 51 units (51 × 7 = 357)
Width: 7 units
So, one possible set of dimensions for the box is: 7 units (height) × 51 units (length) × 7 units (width).
To find the possible dimensions of the box, we want to find three numbers (height, length, and width) that, when multiplied together, equal the given volume of 357.
To solve this, we can start by listing all the possible factors of 357. The factors of 357 are 1, 3, 7, 17, 21, 51, 59, 119, 177, and 357. These numbers can potentially be the dimensions of the box.
We can try each of these numbers as the height and see if we can find two other numbers that, when multiplied together, give us the remaining volume for the box.
Let's start with the first factor, which is 1. Assuming the height of the box is 1, we need to find two numbers whose product is 357.
By checking the remaining factors, we see that 119 and 3 are factors of 357. So, if the height is 1, the length would be 119, and the width would be 3.
Therefore, the possible dimensions of the box are:
Height: 1
Length: 119
Width: 3
Please note that there are multiple possible combinations of dimensions for a given volume, so these dimensions are not the only possibility. You can use the same method to check the other factors of 357 to find other possible dimensions.