(a) Water is poured into a cuboidal reservoir at the rate of 60 litres per minute. If the volume of reservoir is 108 find the number of hours it will take to fill the reservoir. |
(b) If the radius and height of the cylindrical tank are 7 m and 10 m, find the capacity of the tank. |
Answer:
(a) \[\because\] Volume of the reservoir \[=\text{ }108\text{ }{{m}^{3}}\] \[1\text{ }{{m}^{3}}=\text{ }1000\] litres \[\therefore\] Capacity of the reservoir \[=\text{ }108\times 1000\] litres = 108000 litres Amount of water poured in 1 minute = 60 litres \[\therefore\] Amount of water to be poured in 1 hour \[=\text{ }60\text{ }\times \text{ }60\] litres Thus, number of hours required to fill the reservoir \[=\frac{108000}{60\times 60}=30\] \[\therefore\] The required number of hours = 30 (b) Let the radius of cylindrical tank (r) = 7 cm and height (h) = 10 m Then, the capacity of the tank i.e., Volume of the tank \[=\pi {{r}^{2}}h\] \[=\frac{22}{7}\times {{7}^{2}}\times 10\] \[=\frac{22}{7}\times 7\times 7\times 10\,{{m}^{3}}\] \[=\text{ }22\times 7\times 10\text{ }{{m}^{3}}\] \[=\text{ }1540\text{ }{{m}^{3}}\]
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