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

How does doubling the diameter of a circle change its area?

Answer
VerifiedVerified
468.3k+ views
like imagedislike image
Hint: Here, we will find the area of the circle with the given diameter and the area of the circle whose diameter is doubled by using the area of the circle formula. We will use both the area of the circles, to find the change in the area of the circle. Thus, the change in the area of a circle whose diameter is doubled is the required answer.

Formula Used:
We will use the following formula:
1. Radius is half the Diameter i.e.,r=d2
2. Area of the circle is given by A=πr2 where r is the radius of the circle.

Complete step by step solution:
Let us consider a circle whose original diameter is d.
We know that Radius is half the Diameter i.e.,r=d2
We know that the Area of the circle is given by A=πr2 where r is the radius of the circle.
Now, by using the radius of the circle in the area of the circle formula, we get
A=π(d2)2
Applying the exponent on the terms, we get
A=πd24………………………………………………………(1)
seo images

Now, let us consider the circle whose diameter is double the diameter of a circle.
So, we get d1=2d
We know that the Area of the circle is given by A=πr2 where r is the radius of the circle.
Now, by substituting r=d12 in the area of the circle formula, we get
A1=π(d12)2
Substituting d1=2d in above equation, we get
A1=π(2d2)2
Applying the exponent on the terms, we get
A1=4πd24
A1=πd2………………………………………………………(2)
Now, by substituting equation (2) in(1), we get
A=πd24
A=A14
Multiplying 4 on both the sides, we get
A1=4A

Therefore, if the diameter of the circle is doubled, then the area of the circle is four times larger than the area of the circle with diameter d.

Note:
We know that Circle is a two dimensional curve whose distance from the center to any point on the curve is a constant which is called the radius of the circle. Area of a circle is the region occupied by a circle. We should remember that when finding the area of the circle, we will use the radius of the circle and not the diameter of the circle. We should remember that if the diameter is doubled, then the radius is the original diameter.
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