Question

If the radius of the sphere is increased by 25% then what percent its volume and surface area be increases

Answer 1

Explanation:

If radius of sphere is r, volume V is given by 43πr3 and surface area S is 4πr2

Hence V∝r3 and S∝r2 i.e. r∝S12

and hence V∝S32 or S∝V23

as volume rises by 25%, V→1.25V

hence S→S×(1.25)23=1.1604S

i.e. percentage incease in surface area is 16.04%

this is example of this question

Answer 2

Let the original radius of the sphere be r units.

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So, original volume of the sphere will be 4πr³/3 and original surface area will be 4πr².

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If the radius of the sphere is increased by 25% it means that the new radius will be: r + 25% of r = 125r/100.

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So, now we can calculate the volume and surface area of new sphere by taking new radius as 125r/100.

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So, the new volume = 4π(125/100r)³/3 and the new surface area = 4π(125r/100)².

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So, percentage increase in volume

= (new volume - original volume)/original volume × 100

and the percentage increase in surface area = (new surface area - original surface area)/original surface area × 100.

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I have written the main process you can follow. Now, you can put the values and get your solution. This is left to you as an exercise.

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