The radius of a circle has been reduced from 9 cm to 7 cm . the appropriate percentage decrease in area is?

Q: The radius of a circle has been reduced from 9 cm to 7 cm . the appropriate percentage decrease in area is?

Original area = (22/7) x 9 x 9 cm2 New area = (22/7) x 7 x 7 cm2 ∴ Decrease = 22/7 x [(9)2 -(7)2] cm2 =(22/7) x 16 x 2 cm2 Decrease percent = [(22/7 x 16 x 2) /( 7/22 x 9 x 9)] x 100 % = 39.5 %

31.5 %
39.5 %
34.5 %
65.5 %

Correct Answer: 39.5 %

Explanation:

Original area = (22/7) x 9 x 9 cm²
New area = (22/7) x 7 x 7 cm²
∴ Decrease = 22/7 x [(9)² -(7)²] cm²
=(22/7) x 16 x 2 cm²
Decrease percent = [(22/7 x 16 x 2) /( 7/22 x 9 x 9)] x 100 %
= 39.5 %

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