Answer: 64 Cube D's
Explanation:
What we know:
- Cube A has side measurements of 1 cm
- Cube D has side measurements of 1/4 cm
- The formula for the volume of a cube is V = l*w*h
How to solve:
By calculating the volumes of both cubes, we can figure out the maximum amount of Cube D's we can fit in Cube A.
Volume can be calculated by V = l*w*h, where V represents volume in units cubed (u^3), l is length in units, w is width in units, and h is height in units. Our unit is cm- centimeters. Our formula will look like this:
V cm^3 = lcm * wcm * hcm
Process:
Volume of Cube A
Set up equation V = l*w*h
Substitute V = 1 * 1 * 1
Simplify V = 1^3
Solution V = 1 cm^3
Volume of Cube D
Set up equation V = l*w*h
Substitute V = (1/4)*(1/4)*(1/4)
Simplify V = (1/4)^3
Solve V = 0.015625 cm^3
Fitting the Cubes
Where V represents the volume of Cube A, d represents the volume of Cube D, and x represents the number of times Cube D can fit inside of Cube A.
Set up equation V = xd
Substitute 1 = 0.015625x
Change units 1,000,000 = 15,625x
Isolate x /15625 /15625
Solution 64 = x
Answer: 64 Cube D's
Check:
If we multiply Cube D's volume (0.015625 cm^3) by 64, it should equal the volume of Cube A (1 cm^3). Let's test it:
64(0.015625) = 1
1 = 1
Therefore, Cube D can fit into Cube A 64 times.
