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How many liters of water will be contained in a hemispherical bowl whose radius is 2 meters? (1 liter = 1000 cubic cm.)

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16746.66 liters

17646.66 liters

15646.66 liters

16646.66 liters

answer is A.

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Detailed Solution

⇒Volume of hemisphere =

\frac{2}{3} \times π r^{3}

,
1 liter = 1000 cubic cm
1 meter = 100 cm
2 meters = (2×100)cm
⇒ Volume of hemispherical bowl =

\frac{2}{3} \times π \times {(200 cm)}^{3}

We know that π=

\frac{22}{7}

∴Volume of hemispherical bowl =

(\frac{2}{3} \times \frac{22}{7} \times 8000000) c m^{3} .

⇒1000 cubic cm = 1 liter (given)

\Rightarrow 1 cubic cm = \frac{1}{1000} liters \Rightarrow (\frac{2}{3} \times \frac{22}{7} \times 8) c m^{3}

= \frac{\frac{2}{3} \times \frac{22}{7} \times 8000000}{1000} liters

\Rightarrow (\frac{2}{3} \times \frac{22}{7} \times 8) c m^{3}

= (\frac{2}{3} \times \frac{22}{7} \times 8000) liters

This means approximately 16746.666… liters of water can be stored in the water.

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