27. Sheet metal is to be cut from the pattern of Fig. 14-16(a) and bent to form the frustum of a cone [Fig. 14-16(b)], with top and bottom open. Find the dimen- sions r and R and the angle 0 in degrees.
27. Sheet metal is to be cut from the pattern of Fig. 14-16(a) and bent to form the frustum of a cone [Fig. 14-16(b)], with top and bottom open. Find the dimen- sions r and R and the angle 0 in degrees.
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
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![**Problem 27: Sheet Metal Fabrication**
Sheet metal is to be cut from the pattern of Fig. 14-16(a) and bent to form the frustum of a cone [Fig. 14-16(b)], with top and bottom open. Find the dimensions \( r \) and \( R \) and the angle \( \theta \) in degrees.
---
**Explanation of Figures:**
There are two diagrams referenced:
- **Fig. 14-16(a)**: This figure likely illustrates the flat pattern of the sheet metal before it is bent. It may appear as a sector of a circle.
- **Fig. 14-16(b)**: This figure shows the resulting frustum of a cone after the sheet metal is bent. It depicts the 3-dimensional shape with an open top and bottom.
**Objective:**
The task is to calculate:
- \( r \): The radius of the smaller base.
- \( R \): The radius of the larger base.
- \( \theta \): The angle in degrees, likely the sector angle of the flat pattern.
Understanding these calculations will involve geometric principles and possibly trigonometric functions related to the dimensions and angle of a cone's frustum.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F099a3d90-f42c-48d6-a82c-00efefc4d30c%2F55b6fe30-edbe-40c7-a316-ce8b8dfda7ef%2Fnk3si6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 27: Sheet Metal Fabrication**
Sheet metal is to be cut from the pattern of Fig. 14-16(a) and bent to form the frustum of a cone [Fig. 14-16(b)], with top and bottom open. Find the dimensions \( r \) and \( R \) and the angle \( \theta \) in degrees.
---
**Explanation of Figures:**
There are two diagrams referenced:
- **Fig. 14-16(a)**: This figure likely illustrates the flat pattern of the sheet metal before it is bent. It may appear as a sector of a circle.
- **Fig. 14-16(b)**: This figure shows the resulting frustum of a cone after the sheet metal is bent. It depicts the 3-dimensional shape with an open top and bottom.
**Objective:**
The task is to calculate:
- \( r \): The radius of the smaller base.
- \( R \): The radius of the larger base.
- \( \theta \): The angle in degrees, likely the sector angle of the flat pattern.
Understanding these calculations will involve geometric principles and possibly trigonometric functions related to the dimensions and angle of a cone's frustum.
Transcribed Image Text:**Figure 14–16**
This image contains two diagrams representing geometric figures, likely related to a frustum of a cone.
**Diagram (a):**
- Shows a sector of a circle with a central angle labeled as \( \theta \).
- The larger radius of the sector is labeled as \( R \) and the smaller radius as \( r \).
- An arc length is indicated as \( s \).
**Diagram (b):**
- Represents a frustum of a cone.
- The height of the frustum is marked as 350 mm.
- The top circular base has a diameter of 120 mm.
- The bottom circular base has a diameter of 240 mm.
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