R a Consider the region formed by the part of a circle of radius in the first R quadrant and the X-axis. Revolution about the Y-axis of the region V produces a solid hemisphere. Find the volume of the hemisphere by the cylindrical shell method and the disk method. Solution How to approach the problem: Volume of solid of revolution about the Y-axis using the cylindrical shell Sketch the function and the method is solid. Give the equations for the shape of the solid. Find the The equation of the circle is upper and lower limits for the For the region of the circle in the first quadrant bounded region. Evaluation the definite integral to find the volume. = 0 = 0 and the limits of integration are ‘a’ and ‘b’ The volume is QED Volume of solid of revolution about the Y-axis using the disk method is The equation of the circle is For the region of the circle in the first quadrant = 0 = 0 and the limits of integration are ‘a’ and ‘b’ The volume is
How to approach the problem: Sketch the function and the solid. Give the equations for the shape of the solid. Find the upper and lower limits for the bounded region. Evaluation the definite integral to find the volume. Consider the region R formed by the part of a circle of radius a in the first quadrant and the X-axis. Revolution about the Y-axis of the region R produces a solid hemisphere. Find the volume V of the hemisphere by the cylindrical shell method and the disk method. Solution Volume of solid of revolution about the Y-axis using the cylindrical shell method is The equation of the circle is For the region of the circle in the first quadrant and the limits of integration are ‘a’ = 0 and ‘b’ = 0 The volume is QED Volume of solid of revolution about the Y-axis using the disk method is The equation of the circle is For the region of the circle in the first quadrant and the limits of integration are ‘a’ = 0 and ‘b’ = 0 The volume is
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