https://file.aiquickdraw.com/mathbot/file/172609895771857j05ll0.jpg

We are tasked with finding how many gallons of coating are needed for a ring-shaped path around the pool. Let's break down the solution:

### Step 1: Calculate the area of the ring-shaped path
The area of the ring is the difference between the area of the larger circle (outer radius) and the smaller circle (inner radius).

- **Area of a circle** is given by the formula \( A = \pi r^2 \).
  
  - **Outer radius** (\( r_{outer} \)) = 14 yd
  - **Inner radius** (\( r_{inner} \)) = 10 yd

  \[
  A_{outer} = \pi (14)^2 = 3.14 \times 196 = 615.44 \, \text{yd}^2
  \]
  \[
  A_{inner} = \pi (10)^2 = 3.14 \times 100 = 314 \, \text{yd}^2
  \]

- The area of the ring-shaped path is:
  \[
  A_{path} = A_{outer} - A_{inner} = 615.44 - 314 = 301.44 \, \text{yd}^2
  \]

### Step 2: Determine the number of gallons needed
- Each gallon of coating covers **8 yd²**.
- To find the number of gallons required:
  \[
  \text{Gallons needed} = \frac{301.44}{8} = 37.68
  \]

Since the number of gallons must be a whole number, we round up to 38 gallons.

### Final Answer:
You need **38 gallons** of coating.

---

Would you like more details on any of these steps?

Here are five related questions you might find useful:

1. How would the calculation change if the inner radius was larger?
2. What if the coating covered only 5 yd² per gallon?
3. How do you calculate the circumference of the inner and outer circles?
4. How would the required coating change if the pool had a rectangular shape?
5. Could you apply this method to calculate areas of other shapes like ellipses?

**Tip:** Always round up when dealing with materials that need to fully cover a surface!

At the park there is a pool shaped like a circle. A ring-shaped path goes around the pool. Its inner radius is 10 yd and its outer radius is 14 yd. We are going to give a new layer of coating to the path. If one gallon of coating can cover 8 yd², how many gallons of coating do we need? Note that coating comes only by the gallon, so the number of gallons must be a whole number. Use the value 3.14 for π.

Learn how to calculate the gallons of coating required for a ring-shaped path around a circular pool with inner and outer radii of 10 and 14 yards, respectively. The problem involves geometry concepts, including calculating areas of circles and using the formula A = πr².

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation