solid cylinder of height 10 cm and radius 4 cm is to be plated with material costing $11 per cm?. Find the cost of the plates

To find the cost of plating a solid cylinder, we need to calculate its **surface area** (excluding the bases) and then multiply by the given cost per square centimeter.

### Steps:

1. **Surface area of a cylinder (excluding the top and bottom bases):**
   The surface area of the curved part of a cylinder is given by the formula:
   \[
   A = 2 \pi r h
   \]
   where:
   - $ r $ is the radius of the base,
   - $ h $ is the height of the cylinder.

2. **Substitute the given values:**
   - Height $ h = 10 $ cm,
   - Radius $ r = 4 $ cm.

   So, the surface area is:
   \[
   A = 2 \pi (4)(10) = 80 \pi \, \text{cm}^2
   \]
   Approximating $ \pi \approx 3.1416 $:
   \[
   A \approx 80 \times 3.1416 = 251.33 \, \text{cm}^2
   \]

3. **Cost of plating:**
   The cost per cm² is $11. Therefore, the total cost $ C $ is:
   \[
   C = 251.33 \times 11 = 2764.63 \, \text{dollars}
   \]

### Final Answer:
The cost of plating the cylinder is approximately **$2764.63**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How would the cost change if the radius were doubled?
2. What is the total surface area of the entire cylinder including the top and bottom?
3. How much would it cost to plate just the top and bottom of the cylinder?
4. How does the cost change if the material cost increases to $15 per cm²?
5. What would be the cost if the cylinder's height was reduced by half?

**Tip:** Always check if the surface area formula needs to include or exclude the bases, depending on what part of the cylinder is being plated.

A solid cylinder of height 10 cm and radius 4 cm is to be plated with material costing $11 per cm². Find the cost of the plating.

Learn how to calculate the cost of plating a solid cylinder of height 10 cm and radius 4 cm with material costing $11 per cm². This solution covers the surface area formula for the curved part of a cylinder and unit cost calculation. Suitable for Grades 8-10.

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