Final answer:
To find the number of gallons of garbage a cylinder and a hemisphere can hold, calculate the volume of each shape and add them together. Then, divide the total volume by the conversion factor to gallons. The approximate number of gallons they can hold is 0.004.
Step-by-step explanation:
To find the number of gallons of garbage a cylinder and a hemisphere can hold, we first need to find the volume of each shape. The volume of a cylinder is calculated using the formula V = πr²h, where r is the radius and h is the height. The volume of the hemisphere is half the volume of a sphere, which is given by the formula V = (4/3)πr³.
- Let's calculate the volume of the cylinder. Using the given formula, we get V = 3.142 × (0.750 cm)² × 5.25 cm = 9.278 cm³.
- Now, let's find the volume of the hemisphere. Since the volume is half that of a sphere, we can divide the volume by 2. Substituting the values into the formula, we get V = (4/3) × 3.142 × (0.750 cm)³ / 2 = 5.897 cm³.
- Add the volumes of the cylinder and the hemisphere to get the total volume. 9.278 cm³ + 5.897 cm³ = 15.175 cm³.
- Convert the total volume to gallons by dividing by the conversion factor, 3785 cm³/gal. 15.175 cm³ / 3785 cm³/gal = 0.004 gallon.
Hence, the cylinder and hemisphere can hold approximately 0.004 gallons of garbage.