Final answer:
To find the volume of a box that will hold the pizza and the cup of marinara sauce, calculate the volume of each item separately using the formula for the volume of a cylinder, and then add the volumes together.
Step-by-step explanation:
To find the volume of a box that will hold the pizza and the cup of marinara sauce, you need to find the total volume of both items and add them together. Let's say the pizza has a thickness of 2 cm and a diameter of 30 cm, and the cup of marinara sauce has a height of 10 cm and a diameter of 5 cm.
First, calculate the volume of the pizza using the formula for the volume of a cylinder: V = πr²h. The radius (r) is half of the diameter, so r = 15 cm. The height (h) is the thickness of the pizza, which is 2 cm. Substituting the values into the formula, we get V = π(15 cm)²(2 cm) = 450π cm³.
Next, calculate the volume of the cup of marinara sauce. The cup is in the shape of a cylinder, so we use the same formula. The radius (r) is half of the diameter, so r = 2.5 cm. The height (h) is 10 cm. Substituting the values into the formula, we get V = π(2.5 cm)²(10 cm) = 62.5π cm³.