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If a cube's edge is increased by 50%, what is the new volume compared to the ori

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Question: If a cube\'s edge is increased by 50%, what is the new volume compared to the original?

Options:

  1. Increased by 50%
  2. Increased by 125%
  3. Increased by 100%
  4. Increased by 200%

Correct Answer: Increased by 125%

Solution: 

If the edge is increased by 50%, the new edge length is 1.5 times the original. The volume increases by (1.5)³ = 3.375 times, which is an increase of 237.5%.

If a cube's edge is increased by 50%, what is the new volume compared to the ori

Practice Questions

Q1
If a cube's edge is increased by 50%, what is the new volume compared to the original?
  1. Increased by 50%
  2. Increased by 125%
  3. Increased by 100%
  4. Increased by 200%

Questions & Step-by-Step Solutions

If a cube's edge is increased by 50%, what is the new volume compared to the original?
  • Step 1: Understand that a cube has edges of equal length. Let's call the original edge length 'E'.
  • Step 2: If the edge is increased by 50%, the new edge length becomes E + 0.5E, which is 1.5E.
  • Step 3: The volume of a cube is calculated using the formula V = edge length³. So, the original volume is V = E³.
  • Step 4: Now, calculate the new volume using the new edge length: New Volume = (1.5E)³.
  • Step 5: Calculate (1.5)³, which equals 3.375. Therefore, the new volume is 3.375E³.
  • Step 6: To find out how much the volume has increased, compare the new volume (3.375E³) to the original volume (E³).
  • Step 7: The increase in volume is 3.375E³ - E³ = 2.375E³.
  • Step 8: To find the percentage increase, divide the increase (2.375E³) by the original volume (E³) and multiply by 100. This gives (2.375E³ / E³) * 100 = 237.5%.
  • Volume of a Cube – Understanding how the volume of a cube is calculated and how it changes with the edge length.
  • Percentage Increase – Calculating the percentage increase in volume when the edge length is increased.
  • Exponential Growth – Recognizing that volume changes with the cube of the edge length.
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