A party hat is shaped like a cone. The dimensions of the party hat are circumference=6 inches and height=8 inches Which measurement is closest to the volume of the party hat in cubic inches?
A. 75.4 in.^3
B. 301.6 in.^3
C. 402.1 in.^3
D. 100.5 in.^3
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the circumference of the party hat is 6 inches, we can use the formula for the circumference of a circle to find the radius:
Circumference = 2πr
6 = 2πr
r = 3/π
Now we can calculate the volume of the party hat using the given height:
V = (1/3)π(3/π)^2(8)
V = (1/3)π(9/π^2)(8)
V = (24/π) in^3
Approximately, the volume of the party hat is 7.6 in^3, which is closest to option A. 75.4 in.^3.