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
Calculate the surface area of the part above to the nearest tenth of a cm squared. Please complete this neatly and label the different surface areas that you find throughout the problem.
Transcribed Image Text:**Surface Area Calculation Problem**
**Question 11**:
Calculate the surface area of the part above to the nearest tenth of a cm². Please complete this neatly and label the different surface areas that you find throughout the problem.
![### Volume Calculation of a 3D Object
In this section, we will learn how to calculate the volume of a composite 3D object by breaking it down into simpler shapes.
#### Diagram Explanation
The image provided shows a detailed technical drawing of a 3D object. The object seems to consist of a rectangular prism with a semicircular cylindrical cutout. The crucial dimensions provided in the diagram are as follows:
- The main rectangular part of the object has a width of \( 10 \, \text{cm} \), a length of \( 14 \, \text{cm} \), and a height that can be inferred but isn't directly given.
- The semicircular cylindrical cutout has a radius \( R \) of \( 2 \, \text{cm} \) and is positioned such that the total width of the object, including the cutout, is \( 3 \, \text{cm} \).
### Steps to Calculate Volume
1. **Volume of the Rectangular Prism**:
- Volume \( V_{\text{rect}} \) can be calculated using the formula:
\[ V_{\text{rect}} = \text{length} \times \text{width} \times \text{height} \]
- Given dimensions: \( 14 \, \text{cm} \) (length), \( 10 \, \text{cm} \) (width), and \( 3 \, \text{cm} \) (height).
\[ V_{\text{rect}} = 14 \, \text{cm} \times 10 \, \text{cm} \times 3 \, \text{cm} = 420 \, \text{cm}^3 \]
2. **Volume of the Semicircular Cylinder Cutout**:
- The semicircular cylinder has a radius \( R \) of \( 2 \, \text{cm} \) and height \( 3 \, \text{cm} \).
- First, calculate the volume of a full cylinder:
\[ V_{\text{cyl}} = \pi R^2 \times \text{height} \]
- Given radius \( 2 \, \text{cm} \):
\[ V_{\text{cyl}} = \pi \times (2 \, \text{cm})^2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0e9c998a-5af1-4bc2-b298-e1462b059995%2F68a172e2-ee54-4b0c-9608-17023082ca6f%2Fpxs4r4.jpeg&w=3840&q=75)
Transcribed Image Text:### Volume Calculation of a 3D Object
In this section, we will learn how to calculate the volume of a composite 3D object by breaking it down into simpler shapes.
#### Diagram Explanation
The image provided shows a detailed technical drawing of a 3D object. The object seems to consist of a rectangular prism with a semicircular cylindrical cutout. The crucial dimensions provided in the diagram are as follows:
- The main rectangular part of the object has a width of \( 10 \, \text{cm} \), a length of \( 14 \, \text{cm} \), and a height that can be inferred but isn't directly given.
- The semicircular cylindrical cutout has a radius \( R \) of \( 2 \, \text{cm} \) and is positioned such that the total width of the object, including the cutout, is \( 3 \, \text{cm} \).
### Steps to Calculate Volume
1. **Volume of the Rectangular Prism**:
- Volume \( V_{\text{rect}} \) can be calculated using the formula:
\[ V_{\text{rect}} = \text{length} \times \text{width} \times \text{height} \]
- Given dimensions: \( 14 \, \text{cm} \) (length), \( 10 \, \text{cm} \) (width), and \( 3 \, \text{cm} \) (height).
\[ V_{\text{rect}} = 14 \, \text{cm} \times 10 \, \text{cm} \times 3 \, \text{cm} = 420 \, \text{cm}^3 \]
2. **Volume of the Semicircular Cylinder Cutout**:
- The semicircular cylinder has a radius \( R \) of \( 2 \, \text{cm} \) and height \( 3 \, \text{cm} \).
- First, calculate the volume of a full cylinder:
\[ V_{\text{cyl}} = \pi R^2 \times \text{height} \]
- Given radius \( 2 \, \text{cm} \):
\[ V_{\text{cyl}} = \pi \times (2 \, \text{cm})^2
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