A science lab needs a right circular cylindrical container that holds 15 gallons of liquid & is 24in tall. A reference manual states that 231 cubic inches is equivalent to one gallon. What is the approximate radius, in inches, or the container?
Volume = 15*231 = 3465 in^3
= pi*H*R^2 = (75.40 in) R^2
where H is the 24 inch height of the cylinder.
R^2 = 3465/75.4 = 45.95 in^2
R = ___ in
To find the approximate radius of the container, we need to convert the volume from gallons to cubic inches and then use the formula for the volume of a right circular cylinder.
First, we convert 15 gallons to cubic inches by multiplying by the conversion factor:
15 gallons * 231 cubic inches/gallon = 3465 cubic inches
Next, we use the formula for the volume of a cylinder:
Volume = π * radius^2 * height
We can rearrange the formula to solve for the radius:
radius = sqrt(Volume / (π * height))
Plugging in the values, we get:
radius = sqrt(3465 cubic inches / (π * 24 inches))
Now let's calculate the approximate radius using a calculator:
radius ≈ sqrt(3465 / (π * 24)) ≈ sqrt(4.575520833) ≈ 2.138 inches
Therefore, the approximate radius of the container is approximately 2.138 inches.