Question

Observe the measures of pots In the given figure. How many jugs of water can the cylindrical pot hold?

Answer 1

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.