# A pottery jar has circular cross sections of radius 2

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12. A pottery jar has circular cross sections of radius Sketch a picture of the jar and compute its volume. 0 0 0 0
18. Compute the volume of the solid formed by revolving the region bounded by 2 2 , 4 y x y x about (a) the x -axis; (b) y = 4. π 2 ) 2 π
20. Compute the volume of the solid formed by revolving the region bounded by 2 y x and 2 x y about (a) the y -axis; (b) x = 1. π π
b. x = 1 π π
26. Let R be the region bounded by 2 y x and y = 4 . Compute the volume of the solid formed by revolving R about the given line. π 0 π
V = π 2 2 [ 32 12 x 2 + x 4 ] dx = 384/5 π d. y = -2 ===> x = -2 and x = 2 V = π 2 2 [ ( 4 + 2 ) 2 −( 2 + x 2 ) 2 ] dx = π 2 2 [ 36 4 4 x 2 x 4 ] dx V = π 2 2 [ 32 4 x 2 x 4 ] dx = 1408/15 π e. x = 2 ====> y = 4 V = π 0 4 [ ( 2 + y ) 2 ( 2 y ) 2 ] dy = π 0 4 [ ( 2 + y ) 2 ( 2 y ) 2 ] dy V = π 0 4 [ 8 y ] dy = 128/3 π f. x = -4 ===> y = 4 V = π 0 4 [ ( 4 + y ) 2 ( 4 y ) 2 ] dy = π 0 4 [ 16 y ] dy = 256/3 π
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