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1. A triangle has and 25 cm find the exact volume of the Solid of revaution formed when the crecaange is EEREReed about the Side of length n sides that measure 15cm, 20cm triangle revoived 1s

1. A triangle has and 25 cm find the exact volume of the Solid of revaution formed when the crecaange is EEREReed about the Side of length n sides that measure 15cm, 20cm triangle revoived 1s

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 Statement for Volume of Solid of Revolution** **Question:** A triangle has sides that measure 15 cm, 20 cm, and 25 cm. Find the exact volume of the solid of revolution formed when the triangle is revolved about the side of length 15 cm. **Explanation:** This problem requires calculating the volume of a solid generated by rotating the given triangle about one of its sides. Specifically, we need to use techniques from calculus (the method of disks/washers or shells) to find this volume. The triangle in question is a right triangle (since 15^2 + 20^2 = 25^2). Thus, determining the volume involves setting up and evaluating an integral. This problem can be solved using the Pythagorean theorem for verification and then applying integral calculus concepts to find the exact volume. *Steps to Solve:* 1. Verify the triangle is right-angled using the Pythagorean theorem. 2. Set up the integral for the volume of the solid of revolution using either the disk/washer method or the shell method. 3. Evaluate the integral to find the exact volume. This exercise offers practice in geometric visualization, integration techniques, and application of Pythagorean theorem in problem-solving.
Transcribed Image Text:**Problem Statement for Volume of Solid of Revolution** **Question:** A triangle has sides that measure 15 cm, 20 cm, and 25 cm. Find the exact volume of the solid of revolution formed when the triangle is revolved about the side of length 15 cm. **Explanation:** This problem requires calculating the volume of a solid generated by rotating the given triangle about one of its sides. Specifically, we need to use techniques from calculus (the method of disks/washers or shells) to find this volume. The triangle in question is a right triangle (since 15^2 + 20^2 = 25^2). Thus, determining the volume involves setting up and evaluating an integral. This problem can be solved using the Pythagorean theorem for verification and then applying integral calculus concepts to find the exact volume. *Steps to Solve:* 1. Verify the triangle is right-angled using the Pythagorean theorem. 2. Set up the integral for the volume of the solid of revolution using either the disk/washer method or the shell method. 3. Evaluate the integral to find the exact volume. This exercise offers practice in geometric visualization, integration techniques, and application of Pythagorean theorem in problem-solving.
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