If the radius of a circle is increased by 50%, by what percentage will its…
2013
If the radius of a circle is increased by 50%, by what percentage will its perimeter increase?
Answer: D. 50% — ConceptA circle’s circumference is directly proportional to its radius: C = 2πr. Therefore, multiplying the radius by a factor k multiplies the circumference…
- A.
20%
- B.
30%
- C.
40%
- D.
50%
Show answer & explanation
Correct answer: D
Concept
A circle’s circumference is directly proportional to its radius: C = 2πr. Therefore, multiplying the radius by a factor k multiplies the circumference by the same factor k.
Application
Let the original radius be r. Then the original circumference is C = 2πr.
The new radius is r′ = r + 0.50r = 1.50r.
The new circumference is C′ = 2π(1.50r) = 1.50C.
The increase is C′ − C = 0.50C, which is 50% of the original circumference.
Cross-check
For example, if r = 10, then C = 20π. After the increase, r′ = 15 and C′ = 30π. The increase, 10π, is half of 20π, confirming a 50% increase.
Result
The perimeter of the circle increases by 50%.