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sameer sean

· started a discussion

· 1 Months ago

any other solution?? or trick (Question: 181721.0 )

1

Question:
The diameter of a sphere is decreased by 25%. By what percent does its curved surface area decrease?
Options:
A) 43%
B) 43.75%
C) 43.5%
D) 44%
Solution:
Let initial Diameter = 2r1

Final Diameter = 2r1 - \(\cfrac{25}{100}\times\) 2r1

\(\therefore\) Initial curved surface Area = 4\(\pi r_1^2 \)

= \(\pi(2r_1)^2\)

Final curved surface area = \(4\pi r_2^2 \)  

= \(\pi (2r_2)^2\) 

= \(\pi (1.5\ r_1)^2\) 

= 2.25 \(\pi r_1^2 \) 

Decrease in curved surface area 

= \(\cfrac{4\pi r_1^2-2.25\pi r_1^2 }{4\pi r_1^2 }\times100\) 

= \(\cfrac{1.75}{4}\times100= \cfrac{175}{4} = \) 43.75%

Devesh

· commented

· 1 Months ago

fraction of 25% is 1/4 as we know that 4 represent its original value now if d1 is 4 than d2 shoud be 3 now evaluate r1 and r2 which could be 2 and 1.5 now put these two values in the formula of surface area of circle than compare their result. sameer fraction method is the best method to solve the % problem do not more indulge in comlex or real % no just take their fraction no and do the same..

Knowledge Expert

· commented

· 1 Months ago

Dear Student,
Surface area is proportional to square of diameter. If diameter reduces by 25% to 0.75d surface area reduces to 0.5625 of original surface area. thus the reduction is 0.4375, or 43.75%
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sameer sean

· commented

· 1 Months ago

simple solution or trick??
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