If the circumference of a circle increases from 2π to 4 π then its area _____ the original area

(a) Half   (b) Double  (c) Three times   (d) Four times

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  1. Class 10
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Transcript

Question 25 If the circumference of a circle increases from 2πœ‹ to 4 πœ‹ then its area _____ the original area (a) Half (b) Double (c) Three times (d) Four times Now, Old Circumference = 2πœ‹ 2 Γ— πœ‹ Γ— Old Radius = 2πœ‹ Old Radius = πŸπœ‹/πŸπœ‹ Old Radius = 1 Now, (π‘΅π’†π’˜ 𝑨𝒓𝒆𝒂)/(𝑢𝒍𝒅 𝑨𝒂𝒆𝒂)=(πœ‹(𝑁𝑒𝑀 π‘…π‘Žπ‘‘π‘–π‘’π‘ )^2)/(πœ‹(𝑂𝑙𝑑 π‘…π‘Žπ‘‘π‘–π‘’π‘ )^2 ) New Circumference = 4πœ‹ 2 Γ— πœ‹ Γ— New Radius = 4πœ‹ New Radius = πŸ’πœ‹/πŸπœ‹ NEw Radius = 2 =(𝝅 Γ— 𝟐^𝟐)/(𝝅 Γ— 𝟏^𝟐 ) =(πœ‹ Γ— 4)/(πœ‹ Γ— 1) = 4 Thus, New Area = 4 Γ— Old Area So, the correct answer is (d)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.