If the length of an object is doubled, what happens to its volume?
Practice Questions
1 question
Q1
If the length of an object is doubled, what happens to its volume?
It remains the same
It doubles
It triples
It increases by a factor of eight
If the length is doubled, the volume increases by a factor of 2^3 = 8, since volume is proportional to the cube of the length.
Questions & Step-by-step Solutions
1 item
Q
Q: If the length of an object is doubled, what happens to its volume?
Solution: If the length is doubled, the volume increases by a factor of 2^3 = 8, since volume is proportional to the cube of the length.
Steps: 6
Step 1: Understand that volume is calculated using the formula for a cube, which is Volume = length × width × height.
Step 2: If we double the length of the object, we can represent the new length as 2 × original length.
Step 3: Since the object is a cube (or similar shape), if we double the length, we also need to double the width and height to keep the shape the same.
Step 4: Now, the new volume can be calculated as: New Volume = (2 × original length) × (2 × original width) × (2 × original height).
Step 5: This simplifies to New Volume = 2^3 × (original length × original width × original height).
Step 6: Since 2^3 equals 8, the new volume is 8 times the original volume.
