Donna purchased a bucket to make it easier to wash her car. She decided she wanted to paint the inside of the bucket with a design. The bucket has a radius of 7.2
inches and is 15
inches tall.

How many square inches of paint does Donna need to paint the inside of the bucket? Round to the nearest hundredth.
A.678.58
in.2

B.777.6
in.2

C.841.44
in.2

D.1,004.30
in.2

To find the amount of paint Donna needs for the inside of the bucket, we need to calculate the interior surface area of the cylindrical bucket (not including the top, as only the inside needs painting). This means we should include:

1. The area of the **inside curved surface** (the lateral area).
2. The area of the **inside bottom** (a circular base).

### Step 1: Curved Surface Area (Lateral Area)
The formula for the lateral surface area of a cylinder is:

\[
\text{Lateral Area} = 2 \pi r h
\]

where:
- \( r = 7.2 \) inches (radius),
- \( h = 15 \) inches (height).

Substituting in the values:

\[
\text{Lateral Area} = 2 \times \pi \times 7.2 \times 15
\]

\[
\text{Lateral Area} \approx 2 \times 3.1416 \times 7.2 \times 15 \approx 678.58 \text{ in}^2
\]

### Step 2: Bottom Area
The formula for the area of a circle is:

\[
\text{Bottom Area} = \pi r^2
\]

Substituting \( r = 7.2 \) inches:

\[
\text{Bottom Area} = \pi \times (7.2)^2
\]

\[
\text{Bottom Area} \approx 3.1416 \times 51.84 \approx 162.86 \text{ in}^2
\]

### Step 3: Total Surface Area
Now, add the lateral area and the bottom area to get the total interior surface area:

\[
\text{Total Area} = 678.58 + 162.86 = 841.44 \text{ in}^2
\]

### Answer
The amount of paint Donna needs is approximately **841.44 square inches**.

So, the correct answer is:
**C. 841.44 in²**

---

Would you like further details on any part of this process?

### Additional Questions
1. How would the required paint change if the radius were increased by 2 inches?
2. What if the bucket had a lid that also needed painting?
3. How would the paint needed differ if the bucket were half as tall?
4. What’s the effect of using a different unit (e.g., cm²) for area calculation?
5. How does adding thickness to the paint layer affect the calculation?

### Tip
For any cylinder, the lateral area only depends on its height and circumference, making it straightforward to calculate once the height and radius are known.

Donna purchased a bucket to make it easier to wash her car. She decided she wanted to paint the inside of the bucket with a design. The bucket has a radius of 7.2 inches and is 15 inches tall. How many square inches of paint does Donna need to paint the inside of the bucket? Round to the nearest hundredth. A. 678.58 in² B. 777.6 in² C. 841.44 in² D. 1,004.30 in²

Discover how to calculate the interior surface area of a cylinder with a radius of 7.2 inches and a height of 15 inches to find the paint needed for Donna's bucket. This guide explains key geometry concepts, including surface area and cylinder formulas, ideal for Grades 7-9 students.

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