The diameter of a circle is doubled. By how much does the area increas

1.	The diameter of a circle is doubled. By how much does the area increase?1. 2 times2. 4 times3. 8 times4. 16 times
Answer» 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

The diameter of a circle is doubled. By how much does the area increase?1. 2 times2. 4 times3. 8 times4. 16 times

Answer» 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

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