1. Let R be the region shown below; the boundary of R consists of two line segments (one along the r-axis) and a quarter

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1 Let R Be The Region Shown Below The Boundary Of R Consists Of Two Line Segments One Along The R Axis And A Quarter 1 (55.88 KiB) Viewed 22 times

1. Let R be the region shown below; the boundary of R consists of two line segments (one along the r-axis) and a quarter-circle. Let S be the solid of revolution obtained by rotating the region R about the r-axis. (r, s) R 2 (a). Find a formula for the volume V(r, s) of S. (Hint: DON'T do any integration. (b). Use your answer to part (a) to find formulas for V, and Vs. (c). Suppose Theo measures the dimensions of the region R, and obtains the values r = 3 and s = 2. Use Theo's measurements and your answer to part (b) to find V.(3, 2) and V (3,2). (d). Theo reports that his measurements of r and s were approximate, and could be off by 0.5 in either direction. Use your answers above and linear approx- imation/differentials to estimate the maximum possible error in your volume calculation in Dart (c).