The cube in the image has a volume of 1,000 cubic feet. The other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. What is the volume of the tilted solid? O A. 800 cubic feet O B. 1,000 cubic feet OC. 1,200 cubic feet 2,000 cubic féet D.
The cube in the image has a volume of 1,000 cubic feet. The other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. What is the volume of the tilted solid? O A. 800 cubic feet O B. 1,000 cubic feet OC. 1,200 cubic feet 2,000 cubic féet D.
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
Related questions
Question
![### Explaining Volume Formulas: Mastery Test
#### Diagrams:
There are two diagrams depicted in the image.
1. **First Diagram (Cube)**:
- This is a cube with all sides labeled "L".
2. **Second Diagram (Rectangular Prism)**:
- This is a rectangular prism with the height and base the same as the cube ("L"). However, the length of each of its slanted sides is labeled "L + 2".
#### Question:
The question below the diagrams asks:
"The cube in the image has a volume of 1,000 cubic feet. The other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. What is the volume of the tilted solid?"
#### Multiple Choice Options:
- A. 800 cubic feet
- B. 1,000 cubic feet
- C. 1,200 cubic feet
- D. 2,000 cubic feet
#### Selection:
Option **D. 2,000 cubic feet** is selected in the image.
#### Explanation:
To find the volume of the tilted solid (rectangular prism), follow these steps:
1. **Volume of the Cube**:
\[ V = L^3 \]
- Given: Volume of the cube is 1,000 cubic feet.
- Therefore:
\[ L^3 = 1,000 \]
\[ L = 10 \text{ feet} \]
2. **Dimensions of Rectangular Prism**:
- Height (h) = L = 10 feet
- Base (b) = L = 10 feet
- Length (l) = L + 2 = 10 + 2 = 12 feet
3. **Volume of Rectangular Prism**:
\[ V = \text{b} \times \text{h} \times \text{l} \]
\[ V = 10 \times 10 \times 12 \]
\[ V = 1,200 \text{ cubic feet} \]
However, the selection from the multiple choice options shows 2,000 cubic feet, which deviates from this thorough calculation suggesting there might be an error in the pre-selected answer or implying a more complex insight required.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66cd173d-d947-416b-9c02-10ce0e3d2219%2F273445e0-f0d4-4527-979c-e241a047a709%2Fz78nv7fe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Explaining Volume Formulas: Mastery Test
#### Diagrams:
There are two diagrams depicted in the image.
1. **First Diagram (Cube)**:
- This is a cube with all sides labeled "L".
2. **Second Diagram (Rectangular Prism)**:
- This is a rectangular prism with the height and base the same as the cube ("L"). However, the length of each of its slanted sides is labeled "L + 2".
#### Question:
The question below the diagrams asks:
"The cube in the image has a volume of 1,000 cubic feet. The other solid has the same base and height as the cube, but the length of each of its slanted sides is 2 units longer than the height. What is the volume of the tilted solid?"
#### Multiple Choice Options:
- A. 800 cubic feet
- B. 1,000 cubic feet
- C. 1,200 cubic feet
- D. 2,000 cubic feet
#### Selection:
Option **D. 2,000 cubic feet** is selected in the image.
#### Explanation:
To find the volume of the tilted solid (rectangular prism), follow these steps:
1. **Volume of the Cube**:
\[ V = L^3 \]
- Given: Volume of the cube is 1,000 cubic feet.
- Therefore:
\[ L^3 = 1,000 \]
\[ L = 10 \text{ feet} \]
2. **Dimensions of Rectangular Prism**:
- Height (h) = L = 10 feet
- Base (b) = L = 10 feet
- Length (l) = L + 2 = 10 + 2 = 12 feet
3. **Volume of Rectangular Prism**:
\[ V = \text{b} \times \text{h} \times \text{l} \]
\[ V = 10 \times 10 \times 12 \]
\[ V = 1,200 \text{ cubic feet} \]
However, the selection from the multiple choice options shows 2,000 cubic feet, which deviates from this thorough calculation suggesting there might be an error in the pre-selected answer or implying a more complex insight required.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
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.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning