What is the ratio of the volume of water in a cone where the level is half of the height of the cone to the total volume of the cone?

Its pretty easy to calculate. open the top and place a straight edge across the top of the washer, then measure the height in inches from the bottom of the tub to the bottom of the straightedge. Next measure the inner distance from one edge of the tub to the other and cut that number in half. For example: Say the height is 30 inches and the distance across is 28 inches (cut this number in half so use 14). The total cubic inch volume would be calculated like this:

V = 3.1416 x (14 x 14) x 30
3.1416 x 196 x 30
18472.61 cubic inches

Divide 18472.61 by 1728 giving a capacity (volume) of 10.69 cubic feet.

Here is the formula for the volume of a cone. Use it to calculate the volume yourself.
Volume of cone =(1/3)(area of base)*(height)
If the cone is a right circular one
Volume =(1/3)(PI *radius^2)*(height)=(1/3)*Pi*[(3.5)^2]*18.5
assuming that the radius and the height are expressed in the same units. The result (after you calculate it) will be in cubic units.

Volume of right circular cone
V=(Area of base)* height/3=PI*(2.2^2)*(4.3)/3 cm^3
Finish the calculation.

Volume of right circular cone is (1/3)*PI*(r^2)*H
Define real variables r, h
Define constant PI or use built in name.
Prompt for input r=?
Read value and store in r
Prompt for height H=?
Read value and store in H.
Print Volume =, (1/3)PI*r^2*H, unit^3

Volume of right circular cone is (1/3)*PI*(r^2)*H
Define real variables r, h
Define constant PI or use built in name.
Prompt for input r=?
Read value and store in r
Prompt for height H=?
Read value and store in H.
Print Volume =, (1/3)PI*r^2*H, unit^3

Is this a right circular cone or a right circular cylinder?
Volume of cylinder= Pi*(r^2)*h
Volume of cone is 1/3 of volume of cylinder with same height and radius.
Solve for h
h=(Volume)/(PI*r^2) for cylinder

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
r^2=(3V)/(Pi*h)
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.

3 3rd pie * the radius cubed for a sphere

3 3rd pie * the radius squared x the height squared for a cone

3 3rd pie * the perimeter squared x the peak squared for a pyramid

How the hell do you do this?

222500.6668 Ratio