At a party, a coned shape hat is filled with jelly beans. the hat has a diameter of 25.4 centimeters and a height of 18 centimeters. if each jelly bean has a volume of 3.5 cubic centimeters, then how many jelly beans will fit inside the cone shaped hat?
First, calculate the volume of the cone hat using the formula for the volume of a cone:
V = 1/3 * π * r^2 * h
Where V is the volume, r is the radius (half of the diameter), and h is the height.
r = 25.4 cm / 2 = 12.7 cm
V = 1/3 * π * (12.7 cm)^2 * 18 cm
V = 1/3 * π * 161.29 cm^2 * 18 cm
V = 1/3 * 2893.22 cm^3
V = 964.407 cm^3
Now, divide the volume of the cone hat by the volume of each jelly bean to find how many jelly beans will fit inside:
Number of jelly beans = 964.407 cm^3 / 3.5 cm^3
Number of jelly beans ≈ 275.83
Therefore, approximately 275 jelly beans will fit inside the cone-shaped hat.