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Volumes Practice Test 3

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Question : 19 of 40

Marks: +1, -0

A rectangular water tank is 80m × 40m. Water flows into it through a pipe 40

\mathrm{cm}^2

at the opening at a speed of 10 km/hr. By how much, the water level will rise in the tank in half an hour?

$\frac{4}{7}$ cm
$\frac{5}{8}$ cm
$\frac{6}{11}$ cm
$\frac{8}{13}$ cm

Solution:

Concept:

Water flowing through the pipe fills the tank, so volume of water equals tank base area times rise in water level.

Explanation:

Speed

=10\ \text{km/hr}=10\times \frac{5}{18}=\frac{25}{9}\ \text{m/s}

.

Time

=\frac{1}{2}\ \text{hr}=30\times 60=1800\ \text{s}

.

Length of water column

=\frac{25}{9}\times 1800=5000\ \text{m}

.

Pipe area

=40\ \text{cm}^2=\frac{40}{10000}=\frac{1}{250}\ \text{m}^2

.

Volume of water

=5000\times \frac{1}{250}=20\ \text{m}^3

.

Tank base area

=80\times 40=3200\ \text{m}^2

.

Rise

h=\frac{20}{3200}=\frac{1}{160}\ \text{m}

.

Convert to cm:

h=\frac{1}{160}\times 100=\frac{5}{8}\ \text{cm}

.

Answer:

\frac{5}{8}

cm, i.e. option B.

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