if the circumference of the circle increases from 4π to 8π then find the percentage increase in the area of a circle?
Answers
If the circumference of the circle increases from 4π to 8π then the percentage increase in the area of a circle is 300%.
Step-by-step explanation:
Required formula:
- Circumference of the circle, C = 2πr
- Area of the circle, A = πr²
It is given that the circumference of the circle increases from 4π to 8π.
Let the circle with a circumference of 4π have a radius of “r1” and the circle with a circumference of 8π have a radius of “r2”.
Case 1: When circumference is 4π
C = 2πr1
⇒ 4π = 2πr1
⇒ r1 = 2
∴ Area of the circle, A1 = πr1² = π * (2)² = 4π …… (i)
Case 2: When circumference is 8π
C = 2πr2
⇒ 8π = 2πr2
⇒ r2 = 4
∴ Area of the circle, A2 = πr2² = π * (4)² = 16π …… (i)
Thus,
The percentage increase in the area of the circle is given by,
= *100
= [(16π - 4π)/4π] * 100 ….. [substituting from (i) & (ii)]
= [12π/4π] * 100
= 3 * 100
= 300%
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Step-by-step explanation: