The ratio of the radius of two circles is 1 : 4. Find the ratio of the

1.	The ratio of the radius of two circles is 1 : 4. Find the ratio of their areas1. 1 : 162. 1 : 83. 1 : 154. 1 : 64
Answer» Correct Answer - Option 1 : 1 : 16 Given: Ratio of the radius of two circle = 1 : 4 Formula used: Area of circle = πr² Calculation: Let the radius of two circles be x and 4x Area of the first circle = 22/7 × x × x ⇒ 22/7 × x² Area of the second circle = 22/7 × 4x × 4x ⇒ 22/7 × 16x2 Ratio = 22/7 × x² : 22/7 × 16x² ⇒ x² : 16x² ⇒ 1 : 16 ∴ Ratio of their area is 1 : 16

The ratio of the radius of two circles is 1 : 4. Find the ratio of their areas1. 1 : 162. 1 : 83. 1 : 154. 1 : 64

Answer» Correct Answer - Option 1 : 1 : 16

Given:

Ratio of the radius of two circle = 1 : 4

Formula used:

Area of circle = πr²

Calculation:

Let the radius of two circles be x and 4x

Area of the first circle = 22/7 × x × x

⇒ 22/7 × x²

Area of the second circle = 22/7 × 4x × 4x

⇒ 22/7 × 16x2

Ratio = 22/7 × x² : 22/7 × 16x²

⇒ x² : 16x²

⇒ 1 : 16

∴ Ratio of their area is 1 : 16

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The ratio of the radius of two circles is 1 : 4. Find the ratio of their areas1. 1 : 162. 1 : 83. 1 : 154. 1 : 64

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