On decreasing the radius of a circle by 30% its area is decreased by
[a30% [b] 60% [c] 45% [d] none of these
Answers
Answer: [d] none of these
Step-by-step explanation:
Method 1
Decrease area = First area - last area
= pie r ^2 - pie R^2
=pie (100/100)^2- pie (70/100)^2
= 1 - 0.49
=.51
=51%
Method 2
Take r = 10. The area of a circle is (pi)*r^2, therefore the area of a circle with r = 10 is A = (pi)*10^2 = 314.159
Now reducing the radius by 30%, we get R = 7. The area of that circle is A = (pi)*7^2 = 153.938.
153.93/314.159 = .49. Therefore the new area is 49% the size of the old area. Reducing the radius by 30% reduces the area by 51%.
Answer: [d] none of these
Let radius of circle be r.
Area of circle = pi.r^2
Radius decreases = 30%
New radius is r - 50%of r = 0.7 r
New area = 3.14 * (.7r)^2
= 0.49 * 3.14 * r^2
Hence decreasing in area = 51%
Answer : None of these