A rectangular water tank of base \(11\,\text{m}\times 6\,\text{m}\) contains water up to a height of 5 m. If the water is transferred to a cylindrical tank of radius 3.5 m, find the height of water in the cylinder.
\(\displaystyle h=\dfrac{60}{7}\,\text{m}\approx 8.57\,\text{m}\)
Step 1: Write down the dimensions of the rectangular tank.
Length \(= 11\,\text{m}\), Breadth \(= 6\,\text{m}\), Height of water \(= 5\,\text{m}\).
Step 2: Find the volume of water in the rectangular tank.
\(V = \text{length} \times \text{breadth} \times \text{height}\)
\(V = 11 \times 6 \times 5 = 330\,\text{m}^3\).
Step 3: This water is poured into the cylindrical tank, so the volume of water in both tanks is the same.
Step 4: Write the formula for the volume of a cylinder.
\(V = \pi r^2 h\)
Here, radius \(r = 3.5\,\text{m}\), height = \(h\,\text{m}\) (to be found).
Step 5: Substitute values.
\(330 = \pi (3.5)^2 h\)
\(330 = \pi (12.25) h\)
\(330 = 12.25\pi h\)
Step 6: Solve for \(h\).
\(h = \dfrac{330}{12.25\pi}\)
\(h = \dfrac{330}{38.465} \approx 8.57\,\text{m}\).
Step 7: Write the exact simplified fraction.
\(h = \dfrac{60}{7}\,\text{m}\).
Therefore, the height of water in the cylindrical tank is \(\dfrac{60}{7}\,\text{m} \approx 8.57\,\text{m}.\)