Intermediate Algebra
Intermediate Algebra
10th Edition
ISBN: 9781285195728
Author: Jerome E. Kaufmann, Karen L. Schwitters
Publisher: Cengage Learning
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**Find the Length of the Missing Side of a Prism**

To find the length of the missing side of a given prism, follow the instructions below. We have the dimensions of the other two sides and the volume of the prism.

**Given Dimensions:**
- One side: 4 cm
- Second side: 5 cm
- Third side: \( y \) cm (unknown, to be found)
- Volume of the prism: \( 160 \, \text{cm}^3 \)

**Formula for the volume of a rectangular prism:**
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]

Here, the volume of the prism is given, and we need to find the missing side \( y \).

**Calculation Steps:**
1. Substitute the known values into the volume formula:
\[ 160 \, \text{cm}^3 = 4 \, \text{cm} \times 5 \, \text{cm} \times y \, \text{cm} \]
2. Simplify the equation:
\[ 160 = 20 \times y \]
3. Solve for \( y \) by dividing both sides by 20:
\[ y = \frac{160}{20} \]
\[ y = 8 \, \text{cm} \]

**Correct Answer:**
\[ y = 8 \, \text{cm} \]

### Explanation of Graph/Diagram:
The diagram represents a rectangular prism (3D box) with the following labels in the given image:
- The length of one side is labeled as 4 cm.
- The length of another side is labeled as 5 cm.
- The length of the third side is labeled as \( y \) cm, which is unknown.
- The total volume of the prism is stated to be 160 cubic centimeters.

**Multiple Choice Options:** 
- \( \bigcirc \, 2 \, \text{cm} \)
- \( \bigcirc \, 4 \, \text{cm} \)
- \( \bigcirc \, 5 \, \text{cm} \)
- \( \bigcirc \, 6 \, \text{cm} \)
- \( \bigcirc \, 8 \, \text{cm} \) (highlighted indicating it's the chosen answer)

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Transcribed Image Text:**Find the Length of the Missing Side of a Prism** To find the length of the missing side of a given prism, follow the instructions below. We have the dimensions of the other two sides and the volume of the prism. **Given Dimensions:** - One side: 4 cm - Second side: 5 cm - Third side: \( y \) cm (unknown, to be found) - Volume of the prism: \( 160 \, \text{cm}^3 \) **Formula for the volume of a rectangular prism:** \[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \] Here, the volume of the prism is given, and we need to find the missing side \( y \). **Calculation Steps:** 1. Substitute the known values into the volume formula: \[ 160 \, \text{cm}^3 = 4 \, \text{cm} \times 5 \, \text{cm} \times y \, \text{cm} \] 2. Simplify the equation: \[ 160 = 20 \times y \] 3. Solve for \( y \) by dividing both sides by 20: \[ y = \frac{160}{20} \] \[ y = 8 \, \text{cm} \] **Correct Answer:** \[ y = 8 \, \text{cm} \] ### Explanation of Graph/Diagram: The diagram represents a rectangular prism (3D box) with the following labels in the given image: - The length of one side is labeled as 4 cm. - The length of another side is labeled as 5 cm. - The length of the third side is labeled as \( y \) cm, which is unknown. - The total volume of the prism is stated to be 160 cubic centimeters. **Multiple Choice Options:** - \( \bigcirc \, 2 \, \text{cm} \) - \( \bigcirc \, 4 \, \text{cm} \) - \( \bigcirc \, 5 \, \text{cm} \) - \( \bigcirc \, 6 \, \text{cm} \) - \( \bigcirc \, 8 \, \text{cm} \) (highlighted indicating it's the chosen answer) The correct
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