A cube's volume is its edge length cubed. If every edge grows by the same number of centimeters, write the old and new volumes using the same original edge length. Set their difference equal to the given increase, then use a one-variable Desmos regression to find the edge. The trap is stopping at the edge when the question asks for the original volume.
Hints
- Hint 1
A cube's volume is its edge length cubed. Call the original edge centimeters. The added centimeters increase the edge length; they don't multiply it. What are the old and new cube volumes?
- Hint 2
A difference is what remains when you subtract one amount from another. The stated increase is only the added volume, so subtract the original cube's volume from the larger cube's volume.
- Hint 3
An edge length must be positive. Use a Desmos regression to find the original edge from your volume equation, then check what the question asks you to do with that edge.
Step-by-step
Find the original edge with Desmos
Step 1Express the two cube volumes
Let be the original edge length in centimeters. A cube's volume is its edge length cubed, so its original volume is . Because each edge grows by , the new volume is .
- Step 2
Write the increase in volume
New volume minus old volume equals the increase, so:
- Step 3
Find the positive original edge
Enter in Desmos. Here stands for , and tells Desmos to find a value that makes the two sides equal. The restriction keeps the edge positive, since a length can't be negative. The regression shows under PARAMETERS, so the original edge is centimeters.
- Step 4
Find the original volume
The is an edge length, not the requested volume. Add on the next Desmos line; it displays . So the original cube's volume was cubic centimeters. Grid in 343.