To Find: The volume of solid with vertices located at (1,0), (0,1), (-1,0), (0,-1).
The volume of the solid is .
The base of solid is square with vertices located at (1,0), (0,1), (-1,0), (0,-1).
Consider that the solid to the right of the origin .
Radius of the semicircle is .
Find the area of the semicircle using the formula.
Here,r is radius of semicircle.
Expression to find the volume of solid as shown below.
Due to symmetry integrate from 0 to 1 as shown below.
Substitute 0 for a, 1 for b, and for in Equation (1).
Therefore, the volume of the solid is .
To find: the volume of the solid.
the volume of the solid is .
The solid is modified as a cone by cutting method.
Procedure to obtain the volume of solid is explained below.
Find the volume of the cone as shown below.
Substitute 1 for r and 1 for h in Equation (2).
Therefore, the volume of the cone is .
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