How many cubes with 1/2 inch side lengths will fit inside a prism with a volume of 56 cubic inches?
I'm thinking 112, since 56 * 2 =112, but I'm not sure if that's the right thinking.
56 cubes of 1" sides will fit inside the 56in^3 block.
volumes scale as the linear factor cubed, so 8*56 1/2" blocks will fit.
Each 1" cube holds 8 1/2" cubelets.
To determine the number of cubes with 1/2 inch side lengths that will fit inside the prism, we need to find the volume of each cube and then divide the total volume of the prism by the volume of one cube.
The volume of a cube is calculated by raising the length of one side to the power of 3. In this case, the side length of the cube is 1/2 inch, so the volume of one cube is (1/2)^3 = 1/8 cubic inches.
Since the volume of the prism is given as 56 cubic inches, we can divide 56 by 1/8 to find how many cubes can fit inside. Dividing by a fraction is equivalent to multiplying by its reciprocal, so we have:
56 / (1/8) = 56 * (8/1) = 448 cubic inches.
Therefore, 448 cubes with 1/2 inch side lengths will fit inside a prism with a volume of 56 cubic inches.
Your thinking of multiplying the volume (56 cubic inches) by 2 to arrive at 112 does not give the correct result. Instead, we need to calculate the volume of one cube (1/8 cubic inches) and then divide the total volume of the prism (56 cubic inches) by the volume of one cube.