Concept of “Percentage-09”

Question: If radius of a sphere is increased by 20%, then by what percent the surface area of the sphere will be changed? [यदि किसी गोले की त्रिज्या 20% से बढ़ा दी जाये, तो गोले के पृष्ठीय क्षेत्रफल में कितने प्रतिशत का परिवर्तन आएगा?] [Ans. (c) 44%]

(a) 22% (b) 40% (c) 44% (d) 38% (e) None of these   

Solution:

Detailed Explanation: 

First Method: Let the initial area of the sphere is 100 square units. If radius of the sphere is increased by 20%, then there will be two successive changes of 20% each. After the first increase of 20% it will be 100 + 20% of 100 = 100 + 20 = 120. After the second change of 20%, the new area will be 120 + 20% of 120 = 120 + 24 = 144

Area of 100 square units becomes 144 square units. That is, the percentage change in area is (144 – 100)% = 44% Ans.

Second Method: When any quantity is changed by x% and y% successively, then the quantity is changed by

 x + y + xy/100 so, here x + y +xy/100 = (+20) + (+20) +(20)(20)/100) = +40 + 4 = +44. Therefore, 44% Ans.