Storage Tank
A water storage tank has the shape of a cylinder with diameter 3 m.?
A water storage tank has the shape of a cylinder with diameter 3 m.
It is mounted so that the circular cross-sections are vertical. If the depth of the water is 2 m, what percentage of the total capacity is being used?
This is related to integration. But I don't even know where to start???!!!!!How do I do this?
If it's related to integration then you need to create an equation relating the area of a circle to the height across the vertical diameter.
The equation of the circle is x^2+y^2 = 1.5^2
The area in integral terms is the integration of xdy where x is the local horizontal distance from the centre to the circumference and dy is the step in the vertical direction. we know x = sqrt(1.5^2-y^2) so the integration is
sqrt(1.5^2-y^2)dy and the limits are -1.5 to 0.5
This is a standard integral of the form sqrt(a^2-x^2)dx
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