A landscaper is choosing a compost bin. He wants it to hold exactly 12 cubic feet of compost. Using whole numbers only, how many different sizes can he choose from?
assuming rectangular box
1*1*2*2*3 = 12
so
1*1*12
1*2*6
1*3*4
2*2*3
What about 1x2x6 or 2x3x2? Could be more or just four like you said.
To determine the number of different sizes of compost bins the landscaper can choose from, we need to identify the factors of 12, since the volume of a rectangular compost bin can be expressed as the product of its length, width, and height.
The factors of 12 are: 1, 2, 3, 4, 6, and 12.
Since we are looking for whole numbers, we cannot consider fractions or decimals as dimensions for the compost bin. Therefore, the only valid options are the factors that can be combined in pairs to form a product equal to 12.
Let's consider each factor and create pairs:
1 × 12 = 12 (valid pair)
2 × 6 = 12 (valid pair)
3 × 4 = 12 (valid pair)
So, the landscaper has 3 different options for compost bin sizes: 1 cubic foot × 12 cubic feet, 2 cubic feet × 6 cubic feet, and 3 cubic feet × 4 cubic feet.