Let's solve the problems step by step based on the given information.

Part (a):

The volume of a rectangular prism is calculated by: $\text{Volume} = \text{Base Area} \times \text{Height}$

Here:

• Base Area = $17 \frac{1}{4} \, \text{in}^2 = \frac{69}{4} \, \text{in}^2$
• Height = $4 \, \text{in}$

Now, calculate the volume: $\text{Volume} = \frac{69}{4} \times 4 = 69 \, \text{in}^3$

Part (b):

The formula for the volume of a rectangular prism is: $\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}$

Given:

• Volume = $28 \frac{4}{5} \, \text{in}^3 = \frac{144}{5} \, \text{in}^3$
• Length = $6 \, \text{in}$
• Height = $1 \frac{1}{5} \, \text{in} = \frac{6}{5} \, \text{in}$

To find the width, solve for $W$: $\frac{144}{5} = 6 \times W \times \frac{6}{5}$

Simplify: $\frac{144}{5} = \frac{36}{5} \times W$

Multiply both sides by $\frac{5}{36}$: $W = \frac{144}{36} = 4 \, \text{in}$

Summary:

• (a) Volume = $69 \, \text{in}^3$
• (b) Width = $4 \, \text{in}$

Would you like further clarification on any of these steps?

Here are 5 related questions for you:

1. How do you convert mixed fractions to improper fractions?
2. What is the general formula for the volume of a prism?
3. How do you handle operations with fractions in volume calculations?
4. What are some practical applications of calculating the volume of 3D shapes?
5. How would the results change if the base area or height were different?

Tip: When working with mixed fractions, always convert them to improper fractions first for easier calculations.