question_answer

(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

\[=\pi {{r}^{2}}h\]

\[=\frac{22}{7}\times {{7}^{2}}\times 10\]

\[=\frac{22}{7}\times 7\times 7\times 10\,{{m}^{3}}\]

\[=\text{ }22\times 7\times 10\text{ }{{m}^{3}}\]

\[=\text{ }1540\text{ }{{m}^{3}}\]