9. If the surface area of a cylinder with radius of 4 feet is $$ 48 \pi $$ square feet, what is its volume? (A) $$ 1 \pi \mathrm{ft}^{3} $$ (B) $$ 16 \pi \mathrm{ft}^{3} $$ (C) $$ 32 \pi \mathrm{ft}^{3} $$ (D) $$ 48 \pi \mathrm{ft.}^{3} $$ (E) $$ 64 \pi \mathrm{ft.}^{3} $$

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To determine the volume of the cylinder given the surface area and radius, follow these steps:

1. **Understand the Formulas:**
   - **Surface Area of a Cylinder:** $$ S = 2\pi r^2 + 2\pi r h $$
   - **Volume of a Cylinder:** $$ V = \pi r^2 h $$

2. **Given:**
   - Radius ($$ r $$) = 4 feet
   - Surface Area ($$ S $$) = $$ 48\pi $$ square feet

3. **Plug in the Known Values into the Surface Area Formula:**
   $$
   48\pi = 2\pi (4)^2 + 2\pi (4) h
   $$
   $$
   48\pi = 2\pi (16) + 8\pi h
   $$
   $$
   48\pi = 32\pi + 8\pi h
   $$

4. **Solve for Height ($$ h $$):**
   $$
   48\pi - 32\pi = 8\pi h
   $$
   $$
   16\pi = 8\pi h
   $$
   $$
   h = 2 \text{ feet}
   $$

5. **Calculate the Volume:**
   $$
   V = \pi (4)^2 (2) = \pi (16)(2) = 32\pi \text{ cubic feet}
   $$

**Answer:** (C) $$ 32 \pi \mathrm{ft}^{3} $$
The volume of the cylinder is $$ 32 \pi $$ cubic feet.

9. If the surface area of a cylinder with radius of 4 feet is \( 48 \pi \) square feet, what is its volume? (A) \( 1 \pi \mathrm{ft}^{3} \) (B) \( 16 \pi \mathrm{ft}^{3} \) (C) \( 32 \pi \mathrm{ft}^{3} \) (D) \( 48 \pi \mathrm{ft.}^{3} \) (E) \( 64 \pi \mathrm{ft.}^{3} \)

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