How tall would a glass (in the shape of a right circular cylinder) with a diameter of 3 inches need to be to hold 12 oz?
Ounces of what? Water? Metal ball bearings? That weight would translate to different volumes depending on the substance.
Did not specify substance
r= 1/2 diameter
here's the formula for the volume of a right circular cylinder:
V = pi*r^2*h
Find h.
To determine the height of the glass, we need to use the formula for the volume of a right circular cylinder. The formula for the volume is given by:
V = π * r^2 * h
where V is the volume, π is a mathematical constant approximately equal to 3.14159, r is the radius of the circular base (half the diameter), and h is the height of the cylinder.
In this case, the diameter of the glass is given as 3 inches, so the radius (r) would be half of that, which is 1.5 inches.
Now, we need to convert the volume from 12 ounces to cubic inches, since the units need to match. To do this, we can use a conversion factor.
1 fluid ounce is equivalent to 1.80469 cubic inches. So, 12 fluid ounces would be:
Volume = 12 oz * 1.80469 in^3/oz
Now, let's substitute the given values into the formula:
12 * 1.80469 = π * 1.5^2 * h
Simplifying:
21.65628 = 7.06858 * h
Next, we can solve for h by dividing both sides of the equation by 7.06858:
h = 21.65628 / 7.06858
h ≈ 3.06 inches
Therefore, a glass with a diameter of 3 inches would need to be approximately 3.06 inches tall to hold 12 ounces.