Chapter 6 | Applications of Integration
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Figure 6.54 A water tank in the shape of an inverted cone.
The tank starts out full and ends with 4 ft of water left, so, based on our chosen frame of reference, we need to partition the interval [0, 8]. Then, for i =0, 1, 2,…, n , let P ={ x i } be a regular partition of the interval [0, 8], and for i =1, 2,…, n , choose an arbitrary point x i * ∈ [ x i −1 , x i ]. We can approximate the volume of a layer by using a disk, then use similar triangles to find the radius of the disk (see the following figure).
Figure 6.55 Using similar triangles to express the radius of a disk of water.
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