Question

If the radius of a spherical balloon increases by 0.2%. Find the percentage increase in its volume

• A. 0.008
• B. 0.0012
• C. 0.006
• D. 0.003

Answer 1

Answer: (C)

0.006

Answer 2

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 $= \frac{\frac{4}{3} \pi r^{3} \left[\left(1.002\right)^{3} - 1\right]}{\frac{4}{3} \pi r^{3}} \times100$ $= (1.006 - 1) \times 100$ $= 0.006 \times 100 = 0.600 = 0.6$