13. 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?
To calculate the volume of the cylindrical container, we use the formula V = πr^2h, where r is the radius and h is the height.
First, let's find the radius of the cylindrical container:
Radius = diameter/2 = 20 cm / 2 = 10 cm
Now, we can calculate the volume of the cylindrical container:
V = π(10 cm)^2(26 cm)
V = π(100 cm^2)(26 cm)
V = 2600π cm^3
Next, let's calculate the volume of one giant spherical scoop of ice cream:
Radius = diameter/2 = 8 cm / 2 = 4 cm
Volume of one scoop = 4/3 * π * (4 cm)^3
Volume of one scoop = 4/3 * π * 64 cm^3
Volume of one scoop = 268.08 cm^3
Now, let's calculate how many scoops of ice cream we can get from one cylindrical container:
Number of scoops = Volume of container / Volume of one scoop
Number of scoops = 2600π cm^3 / 268.08 cm^3
Number of scoops ≈ 30.5
Therefore, one cylindrical container of ice cream can give Perri approximately 30 scoops of giant spherical ice cream.