
How does doubling the radius of a circle affect its area?
Answer
478.8k+ views
Hint: For this problem we will assume a circle with radius . Now we will calculate the area of the circle which is having the radius and we will denote it as . In the problem they have mentioned that the radius is doubled, so now the radius of the circle will be changed to . Now we will calculate the area of the circle which is having radius and denote it as . To get the result we will establish a relation between the calculated areas and .
Complete step-by-step answer:
Let us assume a circle having the radius which is shown in below figure.
Now the area of the circle having the radius is given by
In the problem they have mentioned that the radius of the circle is doubled. Then the radius of the circle is changed as and the circle is shown in below.
Now the area of the above circle is given by
We have the area of the circle having the radius is . Substituting this value in the above equation, then we will get
Hence, we can say that the area of the circle will be increased by times when the radius is doubled.
Note: In the problem they have mentioned that the radius is doubled. If they have mentioned the radius is increased by times or times. Then also we need to follow the above procedure. But the above procedure is somewhat lengthy, so we have the shorter method i.e., when the radius of the circle is increased by times, then the area will be increased by times.
Complete step-by-step answer:
Let us assume a circle having the radius

Now the area of the circle having the radius
In the problem they have mentioned that the radius of the circle is doubled. Then the radius of the circle is changed as

Now the area of the above circle is given by
We have the area of the circle having the radius
Hence, we can say that the area of the circle will be increased by
Note: In the problem they have mentioned that the radius is doubled. If they have mentioned the radius is increased by
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