Question

If the circumference of a circle is increased by 50%, by
what percent will its area be increased ?​

Answer 1

The increase of the area will be 125%.

• Given data :

The circumference increased by 50%.

• Let, the radius of the circle = x metres (assume x as a variable to perform the further mathematical calculations)

• First, we have to calculate the circumference of the circle

= 2×π×r

= 2πr

• So,the increased circumference of the circle

= 2πr+ (2πr ×50/100)

= 2πr+πr

= 3πr

• Area of the circle

= π×r²

= πr²

Let,the radius of the increased circle = R (assume R as a variable to perform the further mathematical calculation)

So,

2πR = 3πr

2R = 3r

R = 3r/2

So,the area of the new circle

= πR²

= π 9r²/4

= 9πr²/4

So,the increase in the area

= (9πr²/4-πr²)

= (9πr²-4πr²)/4

= 5πr²/4

So,the percentage of increase

= 100×5πr²/4/πr²

= 100×5πr²/4 × 1/πr²

= 125% (answer)

Answer 2

Answer:

125%

Step-by-step explanation:

circumference = 2πr

• So,the increased circumference of the circle

= 2πr+ 1/2(2πr )

= 2πr+πr

= 3πr

• Area of the circle

= πr²

Let,the radius of the increased circle = R

2πR = 3πr

2R = 3r

R = 3r/2

So,the area of the new circle

= πR²

= π 9r²/4

= 9πr²/4

So,the increase in the area

= (9πr²/4-πr²)

= (9πr²-4πr²)/4

= 5πr²/4

So,the percentage of increase

= 100×5πr²/4/πr²

= 100×5πr²/4 × 1/πr²

= 125% (answer)