We are given a spherical fuel tank with an inner diameter of 5.0 feet, and we need to determine how many minutes it will take to drain the tank using a pump that moves 9.48 gallons per minute. Here's the step-by-step approach to solving this problem:

Step 1: Calculate the volume of the sphere

The formula for the volume $V$ of a sphere is:

$V = \frac{4}{3} \pi r^3$

where $r$ is the radius of the sphere. Since the diameter of the sphere is 5.0 feet, the radius $r$ is:

$r = \frac{5.0}{2} = 2.5 \, \text{feet}$

Substitute this into the volume formula:

$V = \frac{4}{3} \pi (2.5)^3$

Step 2: Convert the volume from cubic feet to gallons

1 cubic foot is equivalent to 7.48 gallons, so we will need to multiply the volume we calculate by 7.48 to convert it to gallons.

Step 3: Calculate the time to drain the tank

Once we have the total volume in gallons, we can calculate the time $t$ it will take to drain the tank using the pump rate of 9.48 gallons per minute:

$t = \frac{\text{Total Volume in Gallons}}{\text{Pump Rate (9.48 gallons/min)}}$

Let me compute the exact values for you.It will take approximately 51.64 minutes to drain the spherical fuel tank using the pump.

Would you like further details or have any questions?

Here are some related questions you might consider:

1. How would the time change if the pump rate increased to 12 gallons per minute?
2. What is the volume of the tank in cubic feet before converting to gallons?
3. How does the formula for the volume of a sphere change for different shapes?
4. If the tank's diameter doubled, how long would it take to drain?
5. How can you convert gallons per minute into other units, such as liters per minute?

Tip: Always double-check unit conversions to avoid errors when solving problems involving volume and flow rates.