Question : The radius of a spherical balloon is inflated from 3.5 cm to 4.9 cm by pushing air into it. What is the percentage increase in the volume of the original balloon?
Option 1: 173.6%
Option 2: 174.4%
Option 3: 74.4%
Option 4: 73.6%
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Correct Answer: 174.4%
Solution :
Volume of a sphere = $\frac{4}{3}\pi r^3$, where $r$ is the radius of the sphere.
According to the question
Initial Volume (V
1
) = $\frac{4}{3}\pi(3.5)^{3}$
Final Volume (V
2
) = $\frac{4}{3}\pi(4.9)^{3}$
Now, Percentage increase in volume = $\frac{\frac{4}{3}\pi(4.9)^{3} – \frac{4}{3}\pi(3.5)^{3}}{\frac{4}{3}\pi(3.5)^{3}}$ × 100
= $\frac{(4.9)^{3} – (3.5)^{3}}{(3.5)^{3}}$ × 100
= $\frac{(49)^{3} – (35)^{3}}{(35)^{3}}$ × 100
= $\frac{(7)^{3} – (5)^{3}}{(5)^{3}}$ × 100
= $\frac{343 – 125}{125}$ × 100
= 174.4 %
Hence, the correct answer is 174.4%.
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