Final answer:
To determine the number of gallons of water a sphere with a 7-foot diameter can hold, calculate the volume using the formula for volume of a sphere and convert the resulting cubic feet to gallons resulting in 383.5 gallons, which is option C.
Step-by-step explanation:
To find out how many gallons of water a sphere with a diameter of 7 feet holds, we first calculate the volume of the sphere and then convert that volume into gallons.
Step 1: Calculate the volume of the sphere
The formula for the volume of a sphere is V = (4/3)πr^3, where r is the radius of the sphere. Since the diameter is given as 7 feet, the radius (r) is half of that, which is 3.5 feet.
Step 2: Convert cubic feet to gallons
After calculating the volume in cubic feet, we use the conversion factor that 1 cubic foot equals approximately 7.48 gallons. By multiplying the volume of the sphere in cubic feet by 7.48, we can find the number of gallons the sphere can hold.
Step 3: Calculation and Answer
The volume of the sphere in cubic feet is V = (4/3)π(3.5)^3. After calculating the volume, multiply by 7.48 to convert cubic feet to gallons. This results in the sphere holding approximately 383.5 gallons of water.
Therefore, the correct answer is C. 383.5 gallons.