Question 47
A hemispherical bowl of internal radius 9 cm contains a liquid. This liquid is to be filled into cylindrical shaped small bottles of diameter 1 cm and height 4 cm. How many bottles will be needed to empty the bowl?
Solution
Volume of liquid in bowl = Volume of semi sphere = $$\frac{2}{3}\pi\ r^3$$=$$\frac{2}{3}\pi\ 9^3$$
Volume of each bottle = $$\pi\ r^2h$$ = $$\pi\ \left(\frac{1}{2}\right)^24$$
Let n be the number of bottles needed to fill the liquid.
$$\frac{2}{3}\pi\ 9^3$$ = n*$$\pi\ \left(\frac{1}{2}\right)^24$$
n=$$\frac{2}{3}\cdot9\cdot9\cdot9=2\cdot3\cdot9\cdot9=486$$
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