Question

a farmer connects A pipe of internal diameter 20cm from a Canal into a cylindrical tank in his field which is 10 metre and diameter and 2 metre deep if water flows through the pipe at the rate of 6 kilometre per hour in how much time will the tank be filled​

Answer 1

Answer:

50 minutes

Step-by-step explanation:

r=10 cm=0.1 m

h=?

H of tank=2 m

R of tank=5 m

πR² H=πr² h

π cuts π

5*5*2=0.1*0.1*h

5000 m=h

divide h by speed to get time which is 50 minutes

Answer 2

$\large\sf\red{Internal\:diameter\:of\:pipe=20cm}$

$\implies$$\large\sf\red{\frac{20}{100}m}$

$\implies$$\large\sf\red{0.2m}$

$\large\sf\red{radius=\frac{0.2}{2}=0.1m}$

⠀⠀⠀

$\large\sf\orange{Speed\:of\:water\:flowing\:in\:the\:pipe=3km/h}$

$\implies$$\large\sf\orange{3000m/h}$

⠀⠀

$\large\sf\green{Volume\:of\:water\:that\:flowed\:in\:1hr.+π{r}^{2}h}$

$\implies$$\large\sf\green{π{(0.1)}^{2} \times 3000m}$

$\implies$$\large\sf\green{π×0.01×3000}$

$\implies$$\large\sf\green{{30πm}^{3}}$

⠀⠀

$\large\sf\pink{Volume\:of\:cylindrical\:tank=π{r}^{2}h}$

$\implies$$\small\sf\pink{ππ{(5)}^{2} \times 2}$

⠀⠀

$\large\sf\blue{total \: time \: taken \: by \: pipe \: to \: fill \: the \: tank =}$

$\large\sf\blue{\frac{volume \: of \: cylindrical \: tank}{volume \: of \: water \: flowed \: in \: 1hr.} }$

$\longrightarrow$$\small\sf\blue{\frac{50π}{30π}}$

$\longrightarrow$$\small\sf\blue{\frac{5}{3}hr.}$

$\longrightarrow$$\small\sf\blue{\frac{5}{3}×60\:min.}$

$\longrightarrow$$\small\sf\blue{100\:min.}$