Example 1 Find the volume of a cone of height h and base radius r. Solution A r h 0 (h, 0) Figure 2 A cone is formed by the revolution of the area under the line OA about the x-axis. 107 r r The gradient of the line OA is and the equation of the line OA is y = x. h h If V is the volume of the cone xh  V 2 x0 r 2 2 h h r h3 2  3 h2 1 = 3 units r 2h Example 2 Find the volume of a hemisphere of radius r units. 4 Hence show that the volume of a sphere of radius r is given by 3 Solution
Example 1 Find the volume of a cone of height h and base radius r. Solution A r 0 h (h, 0) Figure 2 A cone is formed by the revolution of the area under the line OA about the x-axis. 107 The gradient of the line OA is r h and the equation of the line OA is y = r h x. If V is the volume of the cone V  xh x0 2 r 2 2 h h  r 2 h3 h2 3 = 1 3 r 2h units Example 2 Find the volume of a hemisphere of radius r units. Hence show that the volume of a sphere of radius r is given by 4 3 Solution
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