Question

If the radius of a sphere is increased by 50%, find the increase percent in volume and the increase percent in the surface area.

Answer 1

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Answer 2

Increased percentage in volume is 237.5% and increased percentage in area is 125%.

Step-by-step explanation:

Since we have given that

Radius of sphere is increased by 50%

Since area contains two r's so, we take it twice, in case of volume, we take r three times.

So, increase percentage in surface area would be

$50+50+\dfrac{50\times 50}{100}\\\\=100+25\\\\=125\%$

So, increased percentage in surface area is 125%.

Similarly,

increased percentage in volume would be

$125+50+\dfrac{125\times 50}{100}\\\\=237.5\%$

Hence, increased percentage in volume is 237.5% and increased percentage in area is 125%.