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, let's calculate the volume of the cylindrical container of ice cream:
Volume = π * r^2 * h
where r is the radius of the container (half of the diameter) and h is the height of the container.
r = 20 cm / 2 = 10 cm
h = 26 cm
Volume = π * 10^2 * 26
Volume = π * 100 * 26
Volume = 2600π cm^3
Next, let's calculate the volume of one giant spherical scoop of ice cream:
Radius of scoop = 8 cm / 2 = 4 cm
Volume of one scoop = 4/3 * π * r^3
Volume of one scoop = 4/3 * π * 4^3
Volume of one scoop = 4/3 * π * 64
Volume of one scoop = 268.086 cm^3
Now, let's find out how many scoops can be obtained from one container:
Number of scoops = Volume of container / Volume of one scoop
Number of scoops = 2600π / 268.086
Number of scoops ≈ 9.69
Therefore, one cylindrical container of ice cream will yield approximately 9 giant spherical scoops of ice cream.