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.

If you keep asking the same question without looking back at the previous responses, your posts will be deleted.

http://www.jiskha.com/display.cgi?id=1309182441

To find the height of a glass with a given diameter that can hold a specific volume, such as 12 ounces, we need to use the formula for the volume of a right circular cylinder.

The formula for the volume of a cylinder is:
Volume = π * radius^2 * height

First, let's convert the diameter of the glass to its radius. The radius is half the diameter. So, the radius of the glass would be 3 inches / 2 = 1.5 inches.

Next, we need to convert the volume from ounces to cubic inches because we are working with inches as the unit of measurement. 1 US fluid ounce is approximately equal to 1.80469 cubic inches. Therefore, 12 ounces * 1.80469 cubic inches/ounce = 21.65628 cubic inches (rounded to the nearest hundredth).

Now, we can plug the values into the volume formula to find the height:
21.65628 cubic inches = π * (1.5 inches)^2 * height

To solve for height, divide both sides of the equation by π * (1.5 inches)^2:
height = 21.65628 cubic inches / (π * (1.5 inches)^2)

Using the value of π as approximately 3.14159, calculate:
height = 21.65628 cubic inches / (3.14159 * (1.5 inches)^2)

Simplifying the equation:
height = 21.65628 cubic inches / (3.14159 * 2.25 inches^2)
height ≈ 21.65628 cubic inches / 14.13716 square inches (rounded to the nearest hundredth)

Dividing the two values:
height ≈ 1.5329 inches

Therefore, a glass with a diameter of 3 inches and a volume of 12 ounces would need to be approximately 1.53 inches tall to hold 12 ounces.