A cube's edge is increased by 50%. What is the percentage increase in its volume

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Question: A cube\'s edge is increased by 50%. What is the percentage increase in its volume?

Options:

Correct Answer: 125%

Solution:

Volume increases by the cube of the increase in edge length. (1.5)³ = 3.375, which is a 237.5% increase.

A cube's edge is increased by 50%. What is the percentage increase in its volume?

A cube's edge is increased by 50%. What is the percentage increase in its volume?

Step 1: Understand that a cube has edges of equal length.
Step 2: Let the original edge length of the cube be 'x'.
Step 3: Calculate the original volume of the cube using the formula: Volume = edge length³. So, original volume = x³.
Step 4: Increase the edge length by 50%. This means the new edge length is x + 0.5x = 1.5x.
Step 5: Calculate the new volume of the cube using the new edge length: New volume = (1.5x)³.
Step 6: Expand the new volume calculation: (1.5x)³ = 1.5³ * x³ = 3.375 * x³.
Step 7: Compare the new volume to the original volume: New volume = 3.375 * x³ and original volume = x³.
Step 8: Find the increase in volume: Increase = New volume - Original volume = 3.375 * x³ - x³ = (3.375 - 1) * x³ = 2.375 * x³.
Step 9: Calculate the percentage increase in volume: Percentage increase = (Increase / Original volume) * 100 = (2.375 * x³ / x³) * 100 = 237.5%.

Volume of a Cube – The volume of a cube is calculated as the cube of its edge length (V = edge³).
Percentage Increase – To find the percentage increase, compare the new volume to the original volume and express the difference as a percentage of the original volume.
Exponential Growth – When a linear dimension (like edge length) is increased, the volume increases exponentially (cubed) relative to that dimension.