Question

find the percentage increase in the volume of a sphere if its radius is increased by 5%


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Answer 1

QUESTION

find the percentage increase in the volume of a sphere if its radius is increased by 5%



ANSWER.



GIVEN


RADIUS OF SPHERE INCREASE 5%



FORMULA USED

$\frac{4}{3} \pi {r}^{3}$



NOW BACK ON QUESTION



LET RADIUS OF SPHERE = r

so

Volume of sphere

$\frac{4}{3} \pi {r}^{3}$

$\pi = \frac{22}{7}$


ACCORDING TO GIVEN CONDITION

R INCREASE 5%


SO RADIUS BECOME

$r + 5\%of \: \: r$



$= > r + \frac{5}{100} r$


$= r + 0.05r$


$1.05r$



NEW VOLUME

$= \frac{4}{3} \pi \times {(1.05 \times r)}^{3}$



$\frac{4}{3} \pi {r}^{3} \times {(1.05)}^{3}$




VOLUME INCREASE=>



$new \: volume - old \: volume$




$\frac{4}{3} \pi {r}^{3} {(1.05)}^{3} - \frac{4}{3} \pi {r}^{3}$




$\frac{4}{3} \pi {r}^{3} ( {(1.05)}^{3} - 1)$



$\frac{4}{3} \pi {r}^{3} (1.15762 - 1)$



$\frac{4}{3} \pi {r}^{3} (0.15762)$



so,

PERCENT INCREASE


$= \frac{volume \: increase}{old \: volume} \times 100$





$\frac{ \frac{4}{3} \pi {r}^{3} \times 0.15762}{ \frac{4}{3}\pi {r}^{3} } \times 100$



$0.1576 \times 100$



$15.76\%$


HENCE INCREASE IN VOLUME IS 15.76%