Capacity of water tank is its volume. The radius of the considered cylindrical tank is 0.35 meters approximately.
What is the volume of a right circular cylinder?
Suppose that the radius of considered right circular cylinder be 'r' units.
And let its height be 'h' units.
Then, its volume is given as:
[tex]V = \pi r^2 h \: \rm unit^3[/tex]
Right circular cylinder is the cylinder in which the line joining center of top circle of the cylinder to the center of the base circle of the cylinder is perpendicular to the surface of its base, and to the top.
(it simply means cylinder is not deformed or leaning, and standing straight on its base).
The capacity of a container is its volume. Thus, for the considered case, we have got:
- Volume of the cylindrical tank = 539 liters.
- Height of the tank = 1.4 meters
- Radius of the base = r meters (say).
Remember that 1 cubic meter = 1000 liters.
Or 1 liters = 1/1000 cubic meters
Thus, x liters = 0.001 times x cubic meters.
Thus, volume of the considered tank in terms of cubic meters is:
[tex]\dfrac{539}{1000} = 0.539 \: \rm m^3[/tex]
(we needed to convert the volume to cubic meters since the height is given in meters, and we always work in one unit, and not mixed units of measurements as they may cause error and confusion).
Thus, using the formula for finding the volume of the cylinder, we get:
[tex]V = \pi r^2 h \: \rm unit^3\\\\\\r^2 = \dfrac{V}{\pi \times h}\\\\r = \sqrt{\dfrac{V}{\pi \times h}}\\\\r = \sqrt{\dfrac{0.539}{\pi \times 1.4}} \approx 0.35 \: \rm meters[/tex]
(took positive square root as radius is non-negative quantity).
Thus, the radius of the considered cylindrical tank is 0.35 meters approximately.
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