Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

Answer 1

Answer:

100 min

Step-by-step explanation:

Given A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

First let us find find the volume of pipe, internal diameter is 20 cm

  So we get the radius as r = d / 2 = 20 / 2 = 10 cm = 1 / 10 m

 Volume of pipe = π r ^2 h

                           = π (1/10) ^2 h

         volume of pipe = π h / 100

Now to find volume of tank which is cylindrical,

  So d = 10 m, r = d / 2 = 5 m and height is 2 m

 Volume of tank = π r ^2 h

                        = π (5) ^2 x 2

      Volume of tank = 50 π

The farmer connects pipe to the tank, so

Volume of pipe = volume of tank

        π h / 100 = 50 π

        h = 50 π x 100 / π

        h = 5 km

Water travels at 3 km / hr

 For 3 kms the time taken for water to travel is 1 hr

  So for 5 kms time taken will be 5 / 3 hrs

     5 / 3 x 60 = 100 minutes

The tank will be filled in 100 minutes

Answer 2

Solution:

As we know pipe is considered as cylinder

internal Radius of pipe = 10 cm = 0.1 m

Let the pipe fill that tank in x hours

length of pipe(height) = 3x km = 3000x m

Volume of pipe
$= \pi \: {r}^{2} \: h \\ \\ = \pi \times 0.1 \times .01 \times 3000x \: \: \: eq1$
Cylindrical tank have radius = 5 m

deep/height = 2 m

Volume =
$\pi \times 5 \times 5 \times 2 \: \: \: eq2$
equate both equations

$\pi \times 0.1 \times0 .1 \times 3000x = \pi \times 25 \times 2 \\ \\ 3000x = \frac{5000}{1 \times 1} \\ \\ x = \frac{5}{3} = 1.6 \: \: hour$
in 1.6 hour that pipe fill the tank.