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 ounces.
To determine the height of the glass, we can use the formula for the volume of a right circular cylinder: V = πr^2h, where V is the volume, r is the radius, and h is the height.
First, we need to find the radius of the glass. Given that the diameter is 3 inches, the radius is half of the diameter, so r = 3/2 = 1.5 inches.
Next, we need to convert the volume from ounces to cubic inches. Since 1 fluid ounce is equivalent to 1.805 cubic inches, we have:
12 ounces * 1.805 cubic inches/ounce = 21.66 cubic inches.
Now, we can plug the values into the formula to find the height:
21.66 cubic inches = π(1.5 inches)^2h.
Simplifying this equation, we have:
21.66 = 2.25πh.
Dividing both sides by 2.25π, we get:
h = 21.66 / (2.25π) ≈ 3.04 inches.
Therefore, the glass would need to be approximately 3.04 inches tall to hold 12 ounces.