7. If the diameter of a circle is increased by
100%. It's area is increased by
1) 100%
2) 200%
3) 300%
4) 400%
Answers
Answer:
May be the answer of this question is 100%.
Hope it's helpful to you.
According to my point of view this is the correct answer.
Answer:
The answer will be 300%.
Step-by-step explanation:
Let the initial diameter be x.
Now the radius (r) = x/2;
Then, area of circle = πr^2;
= 22/7 * (x/2) * (x/2);
= 11x^2/14;
After increasing 100% diameter;
New diameter = (100/100 * x) + x = 2x;
New radius = 2x/2 = x;
Thus, the area of circle with 100% increased diameter = π(x)(x);
= (22/7)*(x)^2;
= 22x^2/7;
Increase in area = (22x^2/7) - (11x^2/14);
= (44x^2 - 11x^2)/14;
= 33x^2/14;
Now, let the increased percent of area be y.
Thus, y% of (11x^2/14) = 33x^2/14;
(y/100) * (11x^2/14) = 33x^2/14;
y = (33x^2/14) / (11x^2/14) * 100;
y = 3 * 100;
y = 300;
Therefore the increased percent of area = 300%;
That's all.