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Triangle ABC is rotated completely around side BC, sweeping out a solid in space. Find the volume of the solid.

AB = 5, AC = 5, CB = 8

 

i dont really get how this works help plz!!

 Mar 27, 2024
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The solid formed by rotating triangle ABC around side BC is a cone. Here's how to find its volume:

 

Identify the cone's dimensions:

 

Radius (r): During the rotation, side AC traces out the base of the cone

 

 Since AC = 5, the base radius (r) of the cone is 5/2 (half the length of AC becomes the radius).

 

Height (h): As the triangle rotates, side AB acts as the height of the cone. Therefore, the height (h) of the cone is 5 (AB length).

 

Formula for Cone Volume: The volume of a cone is calculated using the formula: Volume = (1/3) * π * r^2 * h

 

Substitute Values and Solve: Volume = (1/3) * π * [(5/2)^2] * 5 Volume = (1/3) * π * (25/4) * 5 Volume = (125/12) * π

 

Answer: The volume of the solid is (125/12)π cubic units.

 Mar 27, 2024

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