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If two circles are similar, and the radius of the first circle is 4 cm, what is

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Question: If two circles are similar, and the radius of the first circle is 4 cm, what is the radius of the second circle if the ratio of their areas is 1:4?

Options:

  1. 2 cm
  2. 4 cm
  3. 8 cm
  4. 16 cm

Correct Answer: 8 cm

Solution: 

The area ratio is the square of the radius ratio. If area ratio = 1:4, then radius ratio = 1:2. Therefore, the radius of the second circle = 4 * 2 = 8 cm.

If two circles are similar, and the radius of the first circle is 4 cm, what is

Practice Questions

Q1
If two circles are similar, and the radius of the first circle is 4 cm, what is the radius of the second circle if the ratio of their areas is 1:4?
  1. 2 cm
  2. 4 cm
  3. 8 cm
  4. 16 cm

Questions & Step-by-Step Solutions

If two circles are similar, and the radius of the first circle is 4 cm, what is the radius of the second circle if the ratio of their areas is 1:4?
  • Similarity of Circles – Understanding that similar circles have proportional dimensions, specifically that the ratio of their areas is the square of the ratio of their radii.
  • Area and Radius Relationship – Recognizing that the area of a circle is proportional to the square of its radius, which is crucial for solving problems involving area ratios.
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