The amount of light produced by a cylindrical fluorescent light bulb depends on its lateral area. A certain cylindrical fluorescent light bulb is 36 inches long, has a 1 inch diameter, and is manufactured to produce 0.283 wants of light per square inch. What is the best estimate for the total amount of light that it is able to produce?

Options

A. 32 watts
B. 34 watts
C. 40 watts
D. 48 watts

Answer

To find the total amount of light produced by the cylindrical fluorescent light bulb, we need to follow these steps:

### Step 1: Identify the dimensions of the cylinder
- The length (height) of the cylinder is given as 36 inches.
- The diameter of the cylinder is given as 1 inch, which means the radius (r) is half of the diameter:
\[ r = \frac{1 \text{ inch}}{2} = 0.5 \text{ inches} \]

### Step 2: Calculate the lateral area of the cylinder
- The formula for the lateral area (A) of a cylinder is:
\[ A = 2 \pi r h \]
- Substituting the values of radius (r = 0.5 inches) and height (h = 36 inches):
\[ A = 2 \pi (0.5) (36) = 36 \pi \text{ square inches} \]

### Step 3: Calculate the total amount of light produced
- The light produced per square inch is given as 0.283 watts.
- To find the total light produced, we multiply the lateral area by the light produced per square inch:
\[ \text{Total light} = A \times \text{light per square inch} = (36 \pi) \times 0.283 \]

### Step 4: Calculate the numerical value
- First, calculate \(36 \pi\):
\[ 36 \pi \approx 36 \times 3.14 \approx 113.04 \text{ square inches} \]
- Now, multiply by 0.283:
\[ \text{Total light} \approx 113.04 \times 0.283 \approx 32.0 \text{ watts} \]

### Conclusion
The best estimate for the total amount of light that the cylindrical fluorescent light bulb is able to produce is approximately **32 watts**.

---