Question

Question 7 Using the method of disks/washers, which expression represents the volume of the solid obtained by rotating the region bounded by a = y, y = 1 and x = 0 about the z-axis? son (1 - ſ9) dy • Sor(1 – 2²) ² da None of the other choices S. (1 - y) dy S (1 – 24) de

Answer 1

let us draw the region bounded by the cerves, a=fy, y=1, x=0. Later this region will be notated around x-axis. ay x=59 > y=1 =O 2 2 Gn Z We will method of disks/ washers to obtain the volume. since rotation has been made about a hosizontal anis then the cross-sectional area of the solid will be a function of 's'. Now external sadius wastot 'ge', R(x) = y = l, : x= sy and internal radius wosot 'l', r (21) = y=x². L y=x²] Then the cross-sectional area is, A(21) = T (R²_4²) . i.e, Abx) = 1 (1-24). Hence the volume, v= (A (2) da vf fries (hova)