Advanced Math/Capacity


An old fashioned milk can has the following dimensions:

D = 12 1/8"
d = 7"
h = 16 1/2"
r = 3/4"
t = 4"

Formulate and calculate capacity (in quarts).

Illustration attached.  

One question- Would the figure be considered a cylinder?


Divide the can into sections of different shapes, then find the volume of each section that holds milk.
Finally, convert the total volume from cubic inches into quarts using 1 quart = 57.75 in

The dimensions of the top two sections are incomplete, so assume they do not hold milk. (I think they are the hand grip and lid.)

Divide the rest of the can into three sections:
 one cylinder (blue)
 one sphere segment (red)
 one sphere cap (green)
milk can

Calculate volume of cylinder:
radius r of cylinder = 12⅛2 = 6⅟₁₆ in
height h of cylinder = 16- = 15" in
volume of cylinder = πrh ≅ 1818.6 in

Calculating the volume of the sphere segment is a problem, because we do not know the diameter of its base. It is larger than the cylinder, but we are not told how much larger.
I will use the diameter of the cylinder as an approximation.
r₁ = 72 = 3.5 in
r₂ = 12⅛2 = 6.0625 in
h = 4 in
volume of sphere segment = π(3r₁+3r₂+h)h/6 ≅ 341.4 in

Calculate volume of spherical cap:
r =  6⅟₁₆ in
h = in
volume of sphere cap = π(3r+h)h/6 ≅ 43.5 in

Total volume = 2203.5179 in

Convert to quarts
2203.5179 in 1 qt/(57.75 in) = 38.2 qt

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