Question

if the percentage increase in the area of a circle is 44%,what will be the percentage increase in its circumference​

Answer 1

Answer:

For any 2-dimensional closed shape, any change of some characteristic length of it results in a change in area equal to the square of that change in length.

Let A be the area and L any characteristic length.

IF

A(2) = 1.44 A(1),

THEN

L(2) = √1.44 * L(1) = 1.20 * L(1)

The radius of the circle will have to be increased by 20 %.

Answer 2

FULL EXPLANATION:⬇️

.

Let The radius(r) of Circle be x.

As We Know That,

Area of Circle = π × r²

So,

The Area of Circle = πx²

Circumference of Circle = 2πr

So,

The Circumference of Circle = 2πx

After Increasing,

❥ Area of Circle = πx² + πx² × 44/100

❥ Area of Circle = πx² [1 + 11/25]

❥ Area of Circle = πx² [36/25]

❥ Area of Circle = π {x[6/5]}²

❥ π × R² = π (6x/5)²

[Comparing both sides]

❥ R = 6x/5

So,

The New radius is 6x/5.

As We Know That,

❥ Circumference of New Circle = 2πR

❥ Circumference of New Circle = 2π × 6x/5

❥ Circumference of New Circle = 12πx/5

So,

The Circumference of New Circle is 12πx/5.

As We Know That,

❥ Increase Percentage = Difference/Old Value × 100

❥ Increase Percentage = (12πx/5 - 2πx)/2πx × 100

❥ Increase Percentage = [(12πx - 10πx)/2πx] / 2πx × 100

❥ Increase Percentage = 2πx/5 × 1/2πx × 100

❥ Increase Percentage = 1/5 × 100

❥ Increase Percentage = 20%

So,

The Increase Percentage in Circumference of Circles is 20%.

❐ REQUIRED ANSWER:✅

The Increase Percentage in Circumference of Circles is 20%.⤴️