Question

25. If the circumference of a circle increases from 41 to 87, then find the percentage increase
in the area of the circle.
​

Answer 1

Answer:

the are of circle will also increase at its double ratio

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Answer 2

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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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