![Intermediate Algebra](https://www.bartleby.com/isbn_cover_images/9781285195728/9781285195728_smallCoverImage.gif)
Intermediate Algebra
10th Edition
ISBN: 9781285195728
Author: Jerome E. Kaufmann, Karen L. Schwitters
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Question
thumb_up100%
![**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](https://content.bartleby.com/qna-images/question/a242a625-2826-4f00-ad8f-039422d3d327/a930ae5d-a471-48d0-baab-5c80176c211e/4qdv8js_thumbnail.jpeg)
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
Expert Solution
![Check Mark](/static/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 2 steps with 1 images
![Blurred answer](/static/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Similar questions
- A triangular poster has base 80 centimeters and height 55 centimeters. Find the area of the poster.arrow_forwardWhen the length of each edge of a cube is increased by 1 cm, the volume is increase by 61 cm3. What is the length of each edge of the original cube?arrow_forwardFind the volume of the frustum of a right circular cone with a 155.68-centimeter radius base and a 126.98-centimeter radius base. The frustum height is 24.52 centimeters. Round the answer to the nearest hundredth cubic meter.arrow_forward
- Find the volume of a rectangular room with width 12 feet, length 15 feet, and height 8 feet.arrow_forwardA cylindrical container has a volume of 84 cubic inches and a radius of 3 inches. Find the height of the container.arrow_forwardFind the largest area possible if the association has 1200 feet of fencing available.arrow_forward
- A plate 57.20 millimeters thick is to be machined to a thickness of 44.10 millimeters. The plate is to be rough cut with the last cut a finish cut 0.30 millimeter deep. If each rough cut is 3.20 millimeters deep, how many rough cuts are required?arrow_forwardThe numerical value of the volume of a cube equals the numerical value of its total surface area. What is the length of each edge of the cube?arrow_forwardIn a classroom designed for 30 students, the air conditioning system can move 450 cubic feet of air per minute. (a) Determine the ventilation rate per child in a full classroom. (b) Estimate the air space required per child. (c) Determine the minimum number of square feet of floor space required for the room when the ceiling height is 30 feet.arrow_forward
- Zaidah plans a raised flower bed 2 ft high by 12 ft wide by 15 ft long. The mulch, soil, and peat mixture used to fill the raised bed costs 15.75 per cubic yard. What is the total cost of the ingredients used to fill the raised garden?arrow_forwardPascual is remodeling a house and plans a complete drywall for one 8-foot-high room. Dimensions for the room the floor are 12 ft. by 16 ft. aTo replace the drywall on the 4 walls and ceiling, how many 4 ft by 8 ft sheets of drywall are needed? bIf the cost of the drywall and other materials runs 0.40 per ft2, what does Pascual spend for the drywall and materials?arrow_forwardFarmer Watson wishes to fence a rectangular plot of ground measuring 245 ft by 140 ft. aWhat amount of fencing is needed? bWhat is the total cost of the fencing if it costs 1.59 per foot?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Intermediate AlgebraAlgebraISBN:9781285195728Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningHolt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary AlgebraAlgebraISBN:9780998625713Author:Lynn Marecek, MaryAnne Anthony-SmithPublisher:OpenStax - Rice UniversityMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
![Text book image](https://www.bartleby.com/isbn_cover_images/9781285195728/9781285195728_smallCoverImage.gif)
Intermediate Algebra
Algebra
ISBN:9781285195728
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
![Text book image](https://www.bartleby.com/isbn_cover_images/9780547587776/9780547587776_smallCoverImage.jpg)
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
![Text book image](https://www.bartleby.com/isbn_cover_images/9781938168994/9781938168994_smallCoverImage.gif)
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
Elementary Geometry For College Students, 7e
Geometry
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Cengage,
![Text book image](https://www.bartleby.com/isbn_cover_images/9780998625713/9780998625713_smallCoverImage.jpg)
Elementary Algebra
Algebra
ISBN:9780998625713
Author:Lynn Marecek, MaryAnne Anthony-Smith
Publisher:OpenStax - Rice University
![Text book image](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,