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NISHANT

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· 1 Months ago

. (Question: 111057.0 )

IN Q. AREA OF TANK IS IN CM2 NOT IN M2

Question:
Area of the bottom of rectangular tank is 80 x 40 m2. Water flows into it through a pipe 40 cm2 at the opening at the speed of 10 km per hour. The rise in the level of water in the tank is \(\cfrac{1}{2}\) hours is:
Options:
A) \(\cfrac{3}{2}\) cm
B) \(\cfrac{4}{3}\) cm
C) \(\cfrac{5}{8}\) cm
D) 6 cm
Solution:
Ans: (c) Length of water flowing in \(\cfrac{1}{2}\) hour = 5 km

Area of pipe at opening \(=40\ cm^2=\cfrac{40}{10,000}m^2=\cfrac{1}{250}m^2\)

\(\therefore\) Volume of water flowing in \(\cfrac{1}{2}\) hour =\(5000\times\cfrac{1}{250}=20m^3\)

Area of bottom of tank \(=80\times40=3200\ m^2\) 
\(\therefore\) Depth of water \(=\cfrac{volume}{area}\)

\(=\cfrac{20}{3200}\)

\(=\cfrac{1}{160}m\)

\(=\cfrac{1}{160}\times100\ cm\)

\(=\cfrac{5}{8}\ cm\)

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