Calculate the height of each solid. Round your answers to the nearest tenth if needed. A 17.3 in 6.5 in B 12 mm, What is the difference between "slant height, s, and height, h? e 50⁰ ----

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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**Calculate the height of each solid. Round your answers to the nearest tenth if needed.**

**Diagram A:** A cone with a slant height of 17.3 inches and a radius of 6.5 inches. The height forms a right triangle with the slant height and the radius as the base.

**Diagram B:** A cylinder with an angle of inclination of 50° and a slant height of 12 mm.

**Question:** What is the difference between "slant height, s," and height, h? 

The slant height is the distance from the top of a solid, like a cone, directly down to the edge of the base, forming an angle with the base. The height, h, is the perpendicular distance from the top to the center of the base. 

To calculate the height:
- For the cone (Diagram A), use the Pythagorean theorem: \( h = \sqrt{s^2 - r^2} \), where \( s = 17.3 \) inches and \( r = 6.5 \) inches.
- For the cylinder (Diagram B), the height can be found using trigonometric functions, such as \( h = s \cdot \sin(\theta) \), where \( s = 12 \) mm and \( \theta = 50^\circ \).
Transcribed Image Text:**Calculate the height of each solid. Round your answers to the nearest tenth if needed.** **Diagram A:** A cone with a slant height of 17.3 inches and a radius of 6.5 inches. The height forms a right triangle with the slant height and the radius as the base. **Diagram B:** A cylinder with an angle of inclination of 50° and a slant height of 12 mm. **Question:** What is the difference between "slant height, s," and height, h? The slant height is the distance from the top of a solid, like a cone, directly down to the edge of the base, forming an angle with the base. The height, h, is the perpendicular distance from the top to the center of the base. To calculate the height: - For the cone (Diagram A), use the Pythagorean theorem: \( h = \sqrt{s^2 - r^2} \), where \( s = 17.3 \) inches and \( r = 6.5 \) inches. - For the cylinder (Diagram B), the height can be found using trigonometric functions, such as \( h = s \cdot \sin(\theta) \), where \( s = 12 \) mm and \( \theta = 50^\circ \).
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