The volume, V, of a rectangular prism is determined using the formula V=lwh, where l is the length, w is the width, and h is the height of the prism.

Using this formula, what is the width of a rectangular prism that has a volume of 138.24 cubic inches, a height of 9.6 inches, and a length of 3.2 inches? Round to the nearest tenth.

0.2 inches
4.5 inches
46.1 inches
414.7 inches

To find the width (\(w\)) of a rectangular prism using the given volume (\(V\)), height (\(h\)), and length (\(l\)), we can rearrange the volume formula:

\[ V = l \cdot w \cdot h \]

Solving for \(w\):

\[ w = \frac{V}{l \cdot h} \]

Given:
- \( V = 138.24 \) cubic inches
- \( h = 9.6 \) inches
- \( l = 3.2 \) inches

Substitute these values into the formula:

\[ w = \frac{138.24}{3.2 \cdot 9.6} \]

First, calculate the denominator:

\[ 3.2 \cdot 9.6 = 30.72 \]

Next, divide the volume by this product:

\[ w = \frac{138.24}{30.72} = 4.5 \]

So, the width (\(w\)) of the rectangular prism is:

\[ \boxed{4.5 \text{ inches}} \]

Would you like more details or have any questions?

Here are 5 questions you might want to ask:
1. How do you find the height of a rectangular prism given the volume, length, and width?
2. Can you explain the concept of surface area for a rectangular prism?
3. How would you solve for the length if the volume, width, and height are known?
4. What is the formula for the diagonal of a rectangular prism?
5. How does changing one dimension of a rectangular prism affect its volume?

**Tip:** When solving for a variable in a formula, isolate the variable on one side by performing the inverse operations.

Learn how to find the width of a rectangular prism given its volume, height, and length. Solve for the width using the formula V = lwh, where V is 138.24 cubic inches, height is 9.6 inches, and length is 3.2 inches. Get a step-by-step solution and understand the formula used. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation