Question

Radius of sphere increased by 10% then tsa is increased by what%

Answer 1

since the radius of sphere is increased by 10%
then , obviously it's total surface area (TSA) will also be increased.

total surface area of sphere = 4πr^2

let ,r = r1 = r2,(radius)^2= r^2 = r1× r2

let increase in r1 = a = 10

and increase in r2= b = 10

increase in total surface area

=a + b + ab/100

=10 + 10 + 10×10/100

=20 + 1

=21%

therefore, increase in total surface area will be 21%.
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Your Answer : 21 %
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Answer 2

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Here is the solution:

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Let the original radius be x

Find the new radius:

10% increase = 10%x = 0.1x

New radius = x + 0.1x = 1.1x

Find the original TSA:

TSA = 4πr²

TSA = 4πx²

Find the new TSA

TSA = 4πr²

TSA = 4π(1.1x)²

TSA = 4π(1.21x²)

TSA = 4.84πx²

Find the increase in TSA:

Increased = 4.84πx² - 4πx² = 0.84πx²

Find the increase in percentage:

Percentage increase = 0.84πx²/4πx² x 100 = 21%

Answer: The TSA is increased by 21%

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ALTERNATIVE METHOD (SHORT CUT):

increase in area = increase in radius²

increase in area = ( 1 + 0.1)²

increase in area = ( 1.1)²

increase in area = 1.21

therefore the area is increased by 0.21 times

0.21 = 21%