What is the volume of a cone that has a radius of 3.5 and a height of 18.5?

Assuming you are correct that the radius is 2' 6" and not the diameter.
Convert the inches to centimetres
1" = 2.54 Cms
Radius = 2' 6" = 30" X 2.54 = 76.2 Cms
Height = 5' 2" = 62" X 2.54 = 157.48 Cms
Volume of cylinder = Pi x radius squared x height
3.142 x 76.2 x 76.2 x 157.48 = 2,873,038.9 cc
Divide by 1000 to find how many litres (interest note 1000cc car engine is 1 litre)
2,873,039 cc / 1000 = 2,873 litres

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 cylinder is
V=(Area of base)*height.
If cylinder is circular Area of base =PI*radius^2=Pi*r^2
Volume is V=Pi*(8^2)*6 cm^2
Finish the calculation.

Volume of a right circular cylinder of radius r and height h is
V=PI*(r^2)*h
Figure out which is the radius and which is the height, then plug in the formula above. Result is in cm^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?

(1/3) x pi x radius2 x height x density = pounds

where ::


radius = radius of base in inches

density = pounds per cubic inch

height = height in inches

(or you could use feet, meters, cm, mm for radius & height and use kg for density or wahtever units you wish as long as the units are consistent)

Charlie