Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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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)
The correct](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa242a625-2826-4f00-ad8f-039422d3d327%2Fa930ae5d-a471-48d0-baab-5c80176c211e%2F4qdv8js_processed.jpeg&w=3840&q=75)
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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