find two boxes that will hold HALF as many centimeter cubes as the 3 centimeters by 4 centimeters by 6 centimeters box. what would the dimensions of each box be.
dimensions of the first box
dimensions of the second box.
3 * 4 * 6 = 72
72/2 = 36
3 * 4 * 3 = 36
6 * 2 * 3 = 36
2 by 3 by 4
24
To find the dimensions of the two boxes that will hold half as many centimeter cubes as the 3cm x 4cm x 6cm box, we need to calculate the volume of the larger box and then divide it by 2.
1. Calculate the volume of the larger box:
Volume = length x width x height
Volume = 3cm x 4cm x 6cm
Volume = 72 cm³
2. Divide the volume by 2 to find the volume of each smaller box:
Each smaller box will have a volume of 72 cm³ / 2 = 36 cm³.
Now, we need to find the dimensions of two boxes that have a volume of 36 cm³.
To help us find the dimensions, we can start by listing all the ways to multiply three numbers to get 36.
1 x 1 x 36 = 36
1 x 2 x 18 = 36
1 x 3 x 12 = 36
1 x 4 x 9 = 36
1 x 6 x 6 = 36
2 x 2 x 9 = 36
2 x 3 x 6 = 36
3 x 3 x 4 = 36
Now we choose two combinations that are closest in size to the original box dimensions of 3cm, 4cm, and 6cm, while still having a volume of 36 cm³.
The closest combination in size to the original box dimensions is 3cm, 3cm, and 4cm, which gives us a volume of 3cm x 3cm x 4cm = 36 cm³.
Therefore, the dimensions of the first box will be 3cm x 3cm x 4cm.
The second closest combination in size to the original box dimensions is 2cm, 3cm, and 6cm, which also gives us a volume of 2cm x 3cm x 6cm = 36 cm³.
Therefore, the dimensions of the second box will be 2cm x 3cm x 6cm.