If you make a glass in the shape of a right circular cone (think martini glass) how wide would the glass be if it is 4 inches tall and again holds 12 oz. Round to 2 decimal places. (The width is the circumference).
(does not specify what 12oz are)
To determine the width (circumference) of the glass, where the glass is in the shape of a right circular cone, we need to use the given information about its height and its volume (12 oz).
First, let's assume that the 12 oz mentioned refers to the volume of liquid the glass can hold. Since the volume is given, we can use the formula for the volume of a cone to find the radius.
The formula for the volume of a cone is:
V = (1/3) * π * r² * h
Given:
V = 12 oz
h = 4 inches
Let's convert the volume to a more convenient unit, such as cubic inches. Since 1 oz is equivalent to 1.80469 cubic inches, we can multiply the volume in ounces by this conversion factor:
12 oz * 1.80469 in³/oz = 21.65628 in³
Now, we can rearrange the formula for volume to solve for the radius (r), where the height (h) is known:
21.65628 in³ = (1/3) * π * r² * 4 in
To isolate r², divide both sides of the equation by [(1/3) * π * 4]:
r² = (21.65628 in³) / [(1/3) * π * 4 in]
Simplifying and evaluating this expression, we find:
r² ≈ 5.463 in³ / π
Now, solve for the radius (r) by taking the square root of both sides:
r ≈ √(5.463 in³ / π)
Using a calculator, we find that:
r ≈ 1.483 inches
Finally, to find the width (circumference), we can substitute the radius into the formula for the circumference of a circle:
C = 2 * π * r
C ≈ 2 * π * 1.483 inches
Rounding to 2 decimal places, we get:
C ≈ 9.32 inches
Therefore, the width (circumference) of the glass is approximately 9.32 inches.