Perri’s Ice Cream Shoppe is about to advertise giant spherical scoops of ice cream 8 cm in diameter!
Perri wants to be sure there is enough ice cream and wonders how many scoops can be obtained from each cylindrical container of ice cream. The containers are 20 cm in diameter and 26 cm tall.
Determine the number of scoops of ice cream one container will give her?
First, we need to calculate the volume of the cylindrical container of ice cream:
Volume = πr^2h
r = 20 cm / 2 = 10 cm
h = 26 cm
Volume = π(10 cm)^2(26 cm)
Volume = π(100 cm^2)(26 cm)
Volume = 2600π cm^3
Next, we need to calculate the volume of one giant spherical scoop of ice cream:
Radius of one giant scoop = 8 cm / 2 = 4 cm
Volume of one giant scoop = (4/3)π(4 cm)^3
Volume of one giant scoop = (4/3)π(64 cm^3)
Volume of one giant scoop = 268.09 cm^3
Now we divide the volume of the cylindrical container by the volume of one giant scoop to determine the number of scoops:
Number of scoops = 2600π cm^3 / 268.09 cm^3 ≈ 9.68
Therefore, one container of ice cream will give Perri approximately 9 giant spherical scoops of ice cream.