On increasing the diameter of a circle by 40

Asked by admin @ 16/08/2021 in Math viewed by 321 People

If diameter of a circle is increased by 40%, then its area increase by

(a)96%
(b)40%
(c)80%
(d)48%

Answered by admin @ 16/08/2021

Answer:

Its area increased by 96 %.

Among the given options option (a) 96 % is the correct answer.

Step-by-step explanation:

Given :

Let ‘d’ be the original diameter of a circle.

Original Radius of circle ,r = d/2

Area of original circle, A = πr²

A = π × (d/2)²

A = πd²/4

Area of original circle = πd²/4

New diameter ,D = d + 40% of d

[Given diameter of a circle is increased by 40%]

D = d + (40/100) × d

D = d + 0.4d

D = 1.4 d

Radius of new circle ,R = D/2 = 1.4d/2 = 0.7 d

New area of a circle ,A1 = πR²

A1 = π(0.7d)²

A1 = π × 0.49d²

New area of a circle = π × 0.49d²

Change in area = A1 - A

= π × 0.49d² - πd²/4

= πd²(0.49 - ¼)

= πd²(0.49 × 4 - 1)/4

= πd²(1.96 - 1)/4

= πd²(0.96)/4

Change in area = 0.24 πd²

Percentage increase in area = (change in area/ original area) × 100

= (0.24 πd²/πd²/4) × 100

= (0.24 πd² × 4 /πd²) × 100

= (0.24 × 4) × 100

= 0.96 × 100

= 96 %

Percentage increase in area = 96%

Hence, its area increased by 96 %.

HOPE THIS ANSWER WILL HELP YOU….

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