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 hat?
First, we need to calculate the volume of the cone-shaped hat.
The formula for the volume of a cone is V = (1/3)πr^2h, where r is the radius of the base and h is the height.
Given that the diameter of the hat is 25.4 cm, the radius (r) is half of the diameter, so r = 12.7 cm.
Plugging in the values, we get V = (1/3)π(12.7)^2(18) ≈ 9035.44 cubic centimeters.
Since each jelly bean has a volume of 3.5 cubic centimeters, we can divide the total volume of the hat by the volume of each jelly bean to find out how many jelly beans will fit inside.
9035.44 / 3.5 ≈ 2580
Therefore, approximately 2580 jelly beans will fit inside the cone-shaped hat.