To estimate the surface area and volume of a wine barrel
To estimate the surface area and volume of a wine barrel, the diameter of the barrel is measured at different points along the barrel. The surface area, S, and volume, V, can be determined by:
S = 2π∫0Lrdz and V = π∫0Lr2dz
Use the data given in the table to determine the volume and surface area of the barrel
| z (in.) | -18 | -12 | -6 | 0 | 6 | 12 | 18 |
|---|---|---|---|---|---|---|---|
| d (in.) | 0 | 2.6 | 3.2 | 4.8 | 5.6 | 6 | 6.2 |
(a) Use the composite trapezoidal method.
(b) Use the composite Simpson's 1/3 method.
(c) Use the composite Simpson's 3/8 method.
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