Question:
If the radius of a spherical balloon increases by 0.2%. Find the percentage increase in its volume
If the radius of a spherical balloon increases by 0.2%. Find the percentage increase in its volume
Updated On: Jul 6, 2022
- 0.008
- 0.0012
- 0.006
- 0.003
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The Correct Option is C
Solution and Explanation
Let radius of spherical balloon = r
After increasing 0.2%, radius
$ = r + r \times\frac{0.2}{100} = \frac{1002}{1000} r $
Original volume $= \frac{4}{3} \pi r^{3}$
and New volume $ = \frac{4}{3} \pi\left(\frac{1002}{1000}r\right)^{3} $
$\therefore $ Increased volume
$= \frac{4}{3} \pi \left(\frac{1002}{1000}r\right)^{3} - \frac{4}{3} \pi r^{3} $
$= \frac{4}{3} \pi r^{3} \left[\left(\frac{1002}{1000}\right)^{3} - 1\right] $
$ \therefore $ % increased in volume
$= \frac{\frac{4}{3} \pi r^{3} \left[\left(1.002\right)^{3} - 1\right]}{\frac{4}{3} \pi r^{3}} \times100 $
$= (1.006 - 1) \times 100 $
$= 0.006 \times 100 = 0.600 = 0.6 % $
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