If the perimeter of a circle changed from 4 to 8, then what is the change in its area? Option 1: 300% Option 2: 400% Option 3: 100% Option 4: 200%

Answer: 300%. Solution: Perimeter of a circle = 2 r When perimeter = 4: 2 r_1 = 4 r_1 = 2 When perimeter = 8: 2 r_2 = 8 r_2 = 4 Area of a circle = r^2 A_1 = (2)^2 = 4 A_2 = (4)^2 = 16 % Change = (New - Old)/(Old) x 100 = (16 - 4)/(4) x 100 = (12)/(4) x 100 = 3 x 100 = 300%

Geometry

Circles

Easy

If the perimeter of a circle changed from $4\pi$ to $8\pi$ , then what is the change in its area?

300%

400%

100%

200%

✅ Correct Option: 1

Perimeter of a circle $= 2\pi r$

When perimeter $= 4\pi$ :

$2\pi r_1 = 4\pi$

$r_1 = 2$

When perimeter $= 8\pi$ :

$2\pi r_2 = 8\pi$

$r_2 = 4$

Area of a circle $= \pi r^2$

$A_1 = \pi (2)^2 = 4\pi$

$A_2 = \pi (4)^2 = 16\pi$

$\% \text{ Change} = \dfrac{\text{New} - \text{Old}}{\text{Old}} \times 100$

$= \dfrac{16\pi - 4\pi}{4\pi} \times 100$

$= \dfrac{12\pi}{4\pi} \times 100$

$= 3 \times 100$

$= 300\%$

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