Finding the volume of a mug?
December 24th, 2009 | by admin |I was learning about volume in math today, and I was wondering which one of my coffee mugs held more coffee. My first mug had a diameter of 3.5inches, and a height of 4inches. The formula is pi x radius, squared x height. I’m not concerned about this one, but my other mug has 2 diameters, 3.4inches and 2.3inches, and a height of 6.0inches. How do I find the volume of the second mug?
1st Mug V = pir^2 h= pi * 1.75^2 * 3.5 = pi * 7/4*7/4 *7/2 inches^3 = 33.67cubic inches
2nd Mug I assume the mug has a diameter of 3.4 inches at the bottom and tapers to 2.3 inches at the top.
It use an average for the diameter = (3.4 + 2.3 ) /2 = 5.7/2 = 2.85 inches.
The radius = 1.425 inches. Height = 6 in
V = pi * 1.425^2 * 6 = 38.28 cubic inches
2 Responses to “Finding the volume of a mug?”
By peabody on Dec 25, 2009 | Reply
1st Mug V = pir^2 h= pi * 1.75^2 * 3.5 = pi * 7/4*7/4 *7/2 inches^3 = 33.67cubic inches
2nd Mug I assume the mug has a diameter of 3.4 inches at the bottom and tapers to 2.3 inches at the top.
It use an average for the diameter = (3.4 + 2.3 ) /2 = 5.7/2 = 2.85 inches.
The radius = 1.425 inches. Height = 6 in
V = pi * 1.425^2 * 6 = 38.28 cubic inches
References :
By midtownirene on Dec 25, 2009 | Reply
is the side of the mug curved or straight?
If it’s straight then you would do it in several steps.
the volume of the smaller diameter
the volume of the bigger diameter
the diffference of the two divided in half (the cross section of the larger volume vs. the smaller is a rectangle. the angle of increase divides the rectangle in half, into a triangle.)
Add the smaller volume plus the difference diveided in half - that’s your volume.
References :