Antonio is selling his grandmother's recipe for spaghetti sauce. The sauce is sold in a cylinder-shaped can that has a height of 11 cm and a base with a diameter of 8 cm.
Find the amount of sauce that can fit inside the can. Then, find the amount of paper for a label to wrap around the entire side of the can. Use 3.14 for .
First, we need to find the volume of the cylinder-shaped can, which can be calculated using the formula for the volume of a cylinder: V = πr^2h, where r is the radius and h is the height.
Given that the diameter of the base is 8 cm, the radius is half of the diameter, so r = 4 cm. The height of the can is 11 cm.
V = 3.14 * (4 cm)^2 * 11 cm
V ≈ 3.14 * 16 cm^2 * 11 cm
V ≈ 3.14 * 176 cm^3
V ≈ 552.64 cm^3
Therefore, approximately 552.64 cm^3 of spaghetti sauce can fit inside the can.
Next, to find the amount of paper needed for a label to wrap around the entire side of the can, we need to calculate the circumference of the base of the can. The circumference of a circle can be calculated using the formula C = πd, where d is the diameter.
C = 3.14 * 8 cm
C ≈ 25.12 cm
So, the label will need to be 25.12 cm long in order to wrap around the can.
If the height of the can is 11 cm, then the label will need to be 11 cm tall. Therefore, the amount of paper for the label will be:
25.12 cm * 11 cm ≈ 276.32 cm^2
Approximately 276.32 cm^2 of paper will be needed for the label.