Question

The diameter of a sphere is decreased by 30%. By what percent its surface area decreases?​

Answer 1

Answer:

by 60% because of squares

Answer 2

Let the original diameter be 100 .

Original Surface area = 4/3 πr^3

= 4/3 * 22/7 * 100/2 * 100/2 * 100/2

= 1/3 * 11/7 * 1000000

= 11/7 * 1000000

= 11000000/7

Now , when 30% diameter is decreased it becomes 70 .

New Surface area = 4/3 * 22/7 * 70/2 * 70/2 * 70/2

= 1/3 * 11/7 * 70 * 70 * 70

= 1/3 * 11 * 10 * 70 * 70

= 1/3 * 539000

= 539000/3

So, decrease in surface area = ( New Surface area / Original Surface area ) * 100

= [ (539000/3) / (11000000/7) ] * 100

= [ (539000/3) * (7/11000000) ] * 100

= [ 3773000/33000000 ] * 100

= 0.114 * 100

= 11.4%

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