The problem requires finding (a) the volume and (b) the surface area of a sphere with a radius of 48 ft. We are also asked to use $\pi \approx 3.14$ for calculations.

Step 1: Volume of a Sphere

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

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

Substituting $r = 48$ ft and $\pi = 3.14$:

$V = \frac{4}{3} \times 3.14 \times (48)^3$

Step 2: Surface Area of a Sphere

The formula for the surface area $A$ of a sphere is:

$A = 4 \pi r^2$

Substituting $r = 48$ ft and $\pi = 3.14$:

$A = 4 \times 3.14 \times (48)^2$

I'll calculate both the volume and surface area now.### Results:

• Volume of the sphere: $463011.84$ cubic feet (rounded to the nearest hundredth)
• Surface area of the sphere: $28938.24$ square feet (rounded to the nearest hundredth)

Would you like more details or have any further questions?

Here are five related questions to expand this problem:

1. What is the formula for the circumference of a sphere's great circle?
2. How would the volume change if the radius was doubled?
3. How can we calculate the mass of the sphere if its density is given?
4. How does the surface area change if the radius increases by 25%?
5. What is the relationship between the surface area and volume of a sphere?

Tip: Remember that the surface area of a sphere grows quadratically with the radius, while the volume grows cubically.