The diameter of a circle is doubled. By how much does the area increase?
1. 2 times
2. 4 times
3. 8 times
4. 16 times
1. 2 times
2. 4 times
3. 8 times
4. 16 times
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Correct Answer – Option 2 : 4 times
Formula used :
Area of the circle = π.r2 (where r is the radius of the circle)
Diameter of a circle = 2 × the radius of the circle
Calculations :
Let the diameter be x
So the radius will be 2x
⇒ Area of the original circle = π (2x)2 = 4.π.x2
Now the diameter has been doubled
The new diameter will be 2x
The new radius will be 4x
⇒ Area of the circle with new circle = π.(4x)2 = 16.π.x2
⇒ Area of the new circle : Area of the original circle = 16 : 4
⇒ 4 : 1
∴ the area of the new circle will be 4 times the original circle