What size cone is needed to hold 150 gallons
You need a cone with a volume of 150 gallons.
The volume of a right circular cone is given by the formula
V_cone=(Area of base *height)/3
Since cone is circular , its base is a disk with a certain radius r. The formula becomes PI*(r^2)*h/3
As you see there are two variables, the radius and the height. There is an infinite number of combinations (radius, height) that will give you a total volume of 150 gallons. You can choose the radius (r) and solve for h, or you can choose the height then solve for the radius.
I suggest you convert gallons to cubic feet or to cubic meters then put
V=Pi*(r^2)*h/3 where V is the value of volume after conversion.
If you choose the radius, then to isolate h, h=(3*V)/(Pi*r^2)
If you choose the height, then to solve for r
and r=square root of (3V/(Pi*h))
Now, it is your turn to carry out the rest of the calculation.
It will consist of the value of the radius, and the value of the height.
If the cone is not right circular, the situation becomes more complicated.
Sep 16, 2013 |