If the length of an object is doubled, what happens to its volume?

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Question: If the length of an object is doubled, what happens to its volume?

Options:

Correct Answer: It increases by a factor of eight

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.

If the length of an object is doubled, what happens to its volume?

If the length of an object is doubled, what happens to its volume?

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.

Volume and Length Relationship – Volume of an object is proportional to the cube of its linear dimensions.