A cylindrical water tank of diameter 2.8m and height 4.2m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4m/s. Calculate, in minutes, the time it takes to fill the tank.
A cylindrical water tank of diameter 2.8m and height 4.2m is being fed by a pipe of diameter 7 cm through which water flows at the rate of 4m/s. Calculate, in minutes, the time it takes to fill the tank.

Diameter of cylindrical tank = 2.8 m

radius = 1.4 m

Height = 4.2 m

    \[\begin{array}{*{35}{l}} Volume\text{ }of\text{ }water\text{ }filled\text{ }in\text{ }it\text{ }=\text{ }\pi {{r}^{2}}h  \\ =\text{ }22/7\text{ x }1.4\text{ x }1.4\text{ x }4.2\text{ }{{m}^{3}}  \\ =\text{ }181.104/7\text{ }{{m}^{3}}  \\ =\text{ }25.872\text{ }{{m}^{3}}~\ldots \ldots \text{ }\left( i \right)  \\ \end{array}\]

Diameter of the pipe = 7 cm

the radius (r) = 7/2 cm

let the length of water in the pipe = h1

    \[\begin{array}{*{35}{l}} Volume\text{ }=\text{ }\pi {{r}^{2}}{{h}_{1}}  \\ =\text{ }22/7\text{ x }7/2\text{ x }7/2\text{ x }{{h}_{1}}  \\ =\text{ }77/2{{h}_{1}}~c{{m}^{3}}~\ldots \ldots \text{ }\left( ii \right)  \\ 77/2{{h}_{1}}~c{{m}^{3}}~=\text{ }25.872\text{ x }{{100}^{3}}~c{{m}^{3}}~  \\ \end{array}\]

Selina Solutions Concise Class 10 Maths Chapter 20 ex. 20(G) - 4

h1 = 6720 m

Thus, the time taken at the speed of 4 m per second = 6720/(4 x 60) min = 28 min