Podcast
Questions and Answers
What is the volume of the larger cylinder with a radius of 7 cm and height of 14 cm?
What is the volume of the larger cylinder with a radius of 7 cm and height of 14 cm?
- 3080 cm³ (correct)
- 1028 cm³
- 1400 cm³
- 1540 cm³
What is the volume of the smaller cylinder with a radius of 3 cm and the same height of 14 cm?
What is the volume of the smaller cylinder with a radius of 3 cm and the same height of 14 cm?
- 98 cm³
- 162 cm³ (correct)
- 63 cm³
- 126 cm³
How do you calculate the volume of the remaining solid after carving out the smaller cylinder from the larger one?
How do you calculate the volume of the remaining solid after carving out the smaller cylinder from the larger one?
- Add the volumes of both cylinders
- Subtract the volume of the larger from the smaller
- Subtract the volume of the smaller from the larger (correct)
- Divide the volume of the larger by the smaller
What is the total volume of the remaining solid after removing the smaller cylinder from the larger one?
What is the total volume of the remaining solid after removing the smaller cylinder from the larger one?
If the height of both cylinders were to increase to 20 cm while keeping their radii the same, what would be the new volume of the larger cylinder?
If the height of both cylinders were to increase to 20 cm while keeping their radii the same, what would be the new volume of the larger cylinder?
Study Notes
Problem Overview
- A larger cylinder has a smaller cylinder carved out from its center.
- Both cylinders have the same height.
- The task is to find the volume of the remaining solid after the smaller cylinder is removed.
Key Dimensions
- Larger Cylinder:
- Radius: 7 cm
- Height: 14 cm
- Smaller Cylinder:
- Radius: 3 cm
- Height: 14 cm
Relevant Formulas
- Volume of a Cylinder = π * (radius)^2 * height
Solution Approach
- Calculate the volume of the larger cylinder using the formula.
- Calculate the volume of the smaller cylinder using the formula.
- Subtract the volume of the smaller cylinder from the volume of the larger cylinder to find the volume of the remaining solid.
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Description
Explore the process of calculating the volume of a solid formed by removing a smaller cylinder from a larger one. Using the given dimensions and formulas, you'll learn how to find the volume of the remaining solid left after the smaller cylinder is carved out. This problem encourages critical thinking and application of geometric formulas.
