Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Question
Transcribed Image Text:**Problem 13:** Find the volume of each solid.
**Image (a):**
- Shape: Composite Solid made up of a rectangular prism and a segment of a cylinder.
- Dimensions:
- Length of rectangle: 2 inches.
- Height of rectangle: 6 inches.
- Radius of the cylinder segment: 6 inches.
- Central angle of the cylinder segment: 60 degrees.
**Image (b):**
- Shape: Composite Solid made up of a rectangular prism with a trapezoidal top section.
- Dimensions:
- Width of the base of the prism: 12 cm.
- Height of the base of the prism: 6 cm.
- Width of the top of the trapezoidal section: 10 cm.
- Total height of the trapezoidal section: 6 cm.
- Height from the top parallel side to the base parallel side of the trapezoid: 5 cm.
### Detailed Explanation of Diagrams
**Diagram (a):**
- This diagram represents a solid that consists of a quarter of a cylindrical segment attached to the side of a rectangular prism.
- The rectangular prism has a length of 2 inches and a height of 6 inches.
- The cylindrical segment is a quarter circle with a radius of 6 inches and a central angle of 60 degrees.
**Diagram (b):**
- This diagram represents a solid composed of a rectangular base prism topped with a trapezoidal section.
- The base of the rectangular prism has a width of 12 cm and a height of 6 cm.
- The trapezoidal top section has a width of 10 cm at the top and the overall height is 6 cm.
- The vertical height of the trapezoidal section is given as 5 cm, from the top of the trapezoid to the bottom parallel side.
### Solution Approach
To find the volume of each solid, we need to break down the composite shapes into simpler components, find the volume of each component, and then sum them up.
**For Solid (a):**
1. Find the volume of the rectangular prism.
2. Find the volume of the cylindrical segment (using the area of the sector and then integrating it along the length).
**For Solid (b):**
1. Find the volume of the rectangular prism.
2. Find the volume of the trapezoidal section (considering it can be divided into two simpler shapes:
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