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प्रश्न
Observe the measures of pots In the given figure. How many jugs of water can the cylindrical pot hold?
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उत्तर
The Radius of the conical water jug, r = 3.5 cm
Height of conical water jug, h = 10 cm
The radius of a cylindrical water pot, R = 7 cm
Height of cylindrical water pot, H = 10 cm
∴ The volume of the conical jug = \[\frac{1}{3} \mathrm\pi{r}^{2}\mathrm{h}\]
= \[\frac{1}{3}\times\pi\times3.5^{2}\times10\]
= \[\frac{1}{3}\times3.5^{2}\times10\pi \mathrm{cm}^{3}\]
∴ Volume of the cylindrical water pot = \[\pi\mathrm{R}^{2}\mathrm{H}\]
= \[\pi\times7^{2}\times10\]
=\[\mathrm{49}\times10\pi\mathrm{cm}^{3}\]
∴ Number of jugs = \[\frac{\mathrm{Volume~of~cylindrical~pot}}{\mathrm{Volume~of~conical~jug}}\]
= \[\frac{49\times10\pi}{\frac13\times3.5^{2}\times10\pi}\]
= \[\frac{49\times3}{3.5\times3.5}\]
= \[\frac{49\times3\times100}{35\times35}\]
= 12
∴ The cylindrical pot can hold 12 jugs of water.
