Courses
Courses for Kids
Free study material
Offline Centres
More
Store Icon
Store
seo-qna
SearchIcon
banner

How does doubling the radius of a circle affect its area?

Answer
VerifiedVerified
478.8k+ views
like imagedislike image
Hint: For this problem we will assume a circle with radius r. Now we will calculate the area of the circle which is having the radius r and we will denote it as A1. In the problem they have mentioned that the radius is doubled, so now the radius of the circle will be changed to 2r. Now we will calculate the area of the circle which is having radius 2r and denote it as A2. To get the result we will establish a relation between the calculated areas A1 and A2.

Complete step-by-step answer:
Let us assume a circle having the radius r which is shown in below figure.
seo images

Now the area of the circle having the radius r is given by
A1=πr2
In the problem they have mentioned that the radius of the circle is doubled. Then the radius of the circle is changed as 2r and the circle is shown in below.
seo images

Now the area of the above circle is given by
A2=π(2r)2A2=π(4r2)A2=4πr2
We have the area of the circle having the radius r is A1=πr2. Substituting this value in the above equation, then we will get
A2=4A1
Hence, we can say that the area of the circle will be increased by 4 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 3 times or 4 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 n times, then the area will be increased by n2 times.

Latest Vedantu courses for you
Grade 11 Science PCM | CBSE | SCHOOL | English
CBSE (2025-26)
calendar iconAcademic year 2025-26
language iconENGLISH
book iconUnlimited access till final school exam
tick
School Full course for CBSE students
PhysicsPhysics
ChemistryChemistry
MathsMaths
₹41,848 per year
Select and buy
WhatsApp Banner