on increasing the diameter of a cicle by 40% the area will increase by
Answers
Answer:
Its area increased by 96 %.
Answer:
Its area increased by 96 %.
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 %.