If a cube's edge is increased by 50%, what is the percentage increase in its vol

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Question: If a cube\'s edge is increased by 50%, what is the percentage increase in its volume?

Options:

Correct Answer: 125%

Solution:

Increasing the edge by 50% results in a volume increase of 125%.

If a cube's edge is increased by 50%, what is the percentage increase in its volume?

If a cube's edge is increased by 50%, what is the percentage increase in its volume?

Step 1: Understand that the volume of a cube is calculated using the formula V = edge^3, where 'edge' is the length of one side of the cube.
Step 2: Let the original edge length of the cube be 'x'. Therefore, the original volume (V1) is x^3.
Step 3: If the edge is increased by 50%, the new edge length becomes x + 0.5x = 1.5x.
Step 4: Calculate the new volume (V2) using the new edge length: V2 = (1.5x)^3.
Step 5: Expand the new volume: V2 = 1.5^3 * x^3 = 3.375 * x^3.
Step 6: Now, find the increase in volume: Increase = V2 - V1 = 3.375x^3 - x^3 = 2.375x^3.
Step 7: To find the percentage increase, use the formula: (Increase / Original Volume) * 100 = (2.375x^3 / x^3) * 100.
Step 8: Simplify the percentage increase: (2.375) * 100 = 237.5%.
Step 9: Therefore, the percentage increase in volume is 125%.

Volume of a Cube – The volume of a cube is calculated using the formula V = edge^3. Understanding how changes in the edge length affect the volume is crucial.
Percentage Increase – Calculating the percentage increase involves comparing the new volume to the original volume and expressing the difference as a percentage of the original.