revolved about the side of length 40 m. the altitude has a measure equal to that of 1000 amid is in', find the total area of the

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
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do 19 please

### Educational Text Transcription

#### Problem Descriptions

**18) A triangle has sides that measure 9 m, 40 m, and 41 m. Find the exact volume of the solid of revolution formed when the triangle is revolved about the side of length 40 m.**

**19) For a regular square pyramid, suppose that the altitude has a measure equal to that of the edges of the base. If the volume of the pyramid is \(1000 \text{ in}^3\), find the total area of the pyramid.**

**20) In a right regular pentagonal pyramid, suppose that each base measures 4 cm and that the apothem of the base measures 5 cm. The altitude of the pyramid measures 9 cm.**
   a) Find the total area of the pyramid.
   b) Find the volume of the pyramid.

#### Diagram Explanations

To visually aid in understanding the geometric formations described in the problems, two diagrams of the pyramids are provided.

1. The first diagram shows a regular pentagonal base with each side labeled as 4 cm, and another view illustrates the pyramid with a dashed line representing the apothem of the base measuring 5 cm and the altitude measuring 9 cm.

2. The second diagram depicts a regular pyramid, showcasing its symmetry and the key dimensions outlined—in particular, the base and height which are essential for solving the problem.

These illustrations support the geometrical concepts and assist in comprehending the spatial relationships within the pyramids.
Transcribed Image Text:### Educational Text Transcription #### Problem Descriptions **18) A triangle has sides that measure 9 m, 40 m, and 41 m. Find the exact volume of the solid of revolution formed when the triangle is revolved about the side of length 40 m.** **19) For a regular square pyramid, suppose that the altitude has a measure equal to that of the edges of the base. If the volume of the pyramid is \(1000 \text{ in}^3\), find the total area of the pyramid.** **20) In a right regular pentagonal pyramid, suppose that each base measures 4 cm and that the apothem of the base measures 5 cm. The altitude of the pyramid measures 9 cm.** a) Find the total area of the pyramid. b) Find the volume of the pyramid. #### Diagram Explanations To visually aid in understanding the geometric formations described in the problems, two diagrams of the pyramids are provided. 1. The first diagram shows a regular pentagonal base with each side labeled as 4 cm, and another view illustrates the pyramid with a dashed line representing the apothem of the base measuring 5 cm and the altitude measuring 9 cm. 2. The second diagram depicts a regular pyramid, showcasing its symmetry and the key dimensions outlined—in particular, the base and height which are essential for solving the problem. These illustrations support the geometrical concepts and assist in comprehending the spatial relationships within the pyramids.
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