My Learning Cart
?
Categories
Account

If the radius of a circle is doubled, by what factor does the area of the circle

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: If the radius of a circle is doubled, by what factor does the area of the circle increase?

Options:

  1. 1
  2. 2
  3. 4
  4. 8

Correct Answer: 4

Solution: 

The area of a circle is given by A = πr². If the radius is doubled (r\' = 2r), the new area A\' = π(2r)² = 4πr². Thus, the area increases by a factor of 4.

If the radius of a circle is doubled, by what factor does the area of the circle

Practice Questions

Q1
If the radius of a circle is doubled, by what factor does the area of the circle increase?
  1. 1
  2. 2
  3. 4
  4. 8

Questions & Step-by-Step Solutions

If the radius of a circle is doubled, by what factor does the area of the circle increase?
  • Step 1: Understand the formula for the area of a circle, which is A = πr², where r is the radius.
  • Step 2: Identify what happens when the radius is doubled. If the original radius is r, the new radius will be r' = 2r.
  • Step 3: Substitute the new radius into the area formula. The new area A' will be A' = π(2r)².
  • Step 4: Calculate (2r)². This equals 4r².
  • Step 5: Substitute this back into the area formula: A' = π(4r²) = 4πr².
  • Step 6: Compare the new area A' with the original area A. The original area A = πr².
  • Step 7: To find the factor of increase, divide the new area A' by the original area A: (4πr²) / (πr²) = 4.
  • Step 8: Conclude that the area increases by a factor of 4 when the radius is doubled.
  • Area of a Circle – Understanding the formula A = πr² and how changes in the radius affect the area.
  • Scaling Factors – Recognizing how doubling the radius leads to a squared increase in area.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks