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**Problem 5** For the right circular cylinder, suppose that r = 5 in and h = 6 in. Find the exact and approximate: A) lateral area B) total area C) volume **Diagram Explanation:** 1. **Lateral Area (A):** - The sketch of a right circular cylinder is presented with the height (h) marked as 6 in and the radius (r) marked as 5 in. The lateral surface of the cylinder (curved surface area) needs to be calculated. 2. **Total Area (B):** - This involves finding the sum of the lateral area and the area of the two bases (top and bottom circles) of the cylinder. 3. **Volume (C):** - This involves calculating the volume of the cylinder using the given radius and height. The diagram of the cylinder shows dimensions labeled with arrows indicating the height (H) and the top elevated oval representing the circular top of the cylinder. A conceptual illustration depicting the perimeter and height of the cylinder wrapped in a rectangular sheet can be seen at the bottom of the image, aiding in understanding the formula for the lateral area. This problem uses geometry principles specific to cylinders in mathematics to compute surface areas and volume using the given dimensions.

**Problem 5** For the right circular cylinder, suppose that r = 5 in and h = 6 in. Find the exact and approximate: A) lateral area B) total area C) volume **Diagram Explanation:** 1. **Lateral Area (A):** - The sketch of a right circular cylinder is presented with the height (h) marked as 6 in and the radius (r) marked as 5 in. The lateral surface of the cylinder (curved surface area) needs to be calculated. 2. **Total Area (B):** - This involves finding the sum of the lateral area and the area of the two bases (top and bottom circles) of the cylinder. 3. **Volume (C):** - This involves calculating the volume of the cylinder using the given radius and height. The diagram of the cylinder shows dimensions labeled with arrows indicating the height (H) and the top elevated oval representing the circular top of the cylinder. A conceptual illustration depicting the perimeter and height of the cylinder wrapped in a rectangular sheet can be seen at the bottom of the image, aiding in understanding the formula for the lateral area. This problem uses geometry principles specific to cylinders in mathematics to compute surface areas and volume using the given dimensions.

Elementary Geometry For College Students, 7e
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 5** For the right circular cylinder, suppose that r = 5 in and h = 6 in. Find the exact and approximate: A) lateral area B) total area C) volume **Diagram Explanation:** 1. **Lateral Area (A):** - The sketch of a right circular cylinder is presented with the height (h) marked as 6 in and the radius (r) marked as 5 in. The lateral surface of the cylinder (curved surface area) needs to be calculated. 2. **Total Area (B):** - This involves finding the sum of the lateral area and the area of the two bases (top and bottom circles) of the cylinder. 3. **Volume (C):** - This involves calculating the volume of the cylinder using the given radius and height. The diagram of the cylinder shows dimensions labeled with arrows indicating the height (H) and the top elevated oval representing the circular top of the cylinder. A conceptual illustration depicting the perimeter and height of the cylinder wrapped in a rectangular sheet can be seen at the bottom of the image, aiding in understanding the formula for the lateral area. This problem uses geometry principles specific to cylinders in mathematics to compute surface areas and volume using the given dimensions.
Transcribed Image Text:**Problem 5** For the right circular cylinder, suppose that r = 5 in and h = 6 in. Find the exact and approximate: A) lateral area B) total area C) volume **Diagram Explanation:** 1. **Lateral Area (A):** - The sketch of a right circular cylinder is presented with the height (h) marked as 6 in and the radius (r) marked as 5 in. The lateral surface of the cylinder (curved surface area) needs to be calculated. 2. **Total Area (B):** - This involves finding the sum of the lateral area and the area of the two bases (top and bottom circles) of the cylinder. 3. **Volume (C):** - This involves calculating the volume of the cylinder using the given radius and height. The diagram of the cylinder shows dimensions labeled with arrows indicating the height (H) and the top elevated oval representing the circular top of the cylinder. A conceptual illustration depicting the perimeter and height of the cylinder wrapped in a rectangular sheet can be seen at the bottom of the image, aiding in understanding the formula for the lateral area. This problem uses geometry principles specific to cylinders in mathematics to compute surface areas and volume using the given dimensions.
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