27.Find the area inside one loop of the r2= cos2θ and identify thecurveA. 1/2 ; lemniscateC. 9/2 ; cardioidB. 16 : limaconD. π/8 ; four-leaved rose28.Find the length of the arc of y=lnsecx from x=0 to x=π/3.29.Find the arclength of the spiral r=eθfromθ =0 to θ =In2.30.A solid has its base the circle x^2+y^2=9, and all cross sectionsparallel to the y-axis are squares. Find the volume of the solid.B. 344D. 11231.Find the average value of 1/x on [3, 5].32.A particle moves on a straight line with a velocity v = (4 – 2t)^3 attime t. Find the distance traveled from t = 0 to t = 3.33.Find the volume of the solid of revolution formed by revolving theregion bounded by y = x3+ 3, x = 0, x = 1 and y = 0 about x = 1.34.A conical tank, 10meters deep and 8 meters across at the top, isfilled with water to a depth of 5 meters. The tank is emptied bypumping the water over the top edge. How much work is done inthe process?A. 5283 kJC. 4580 kJB. 1625 kJD. 1283 kJ35.Find the differential equations of the family of lines passingthrough the origin.A. xdx – ydy = 0C. xdx + ydy = 0B. xdy – ydx = 0D. ydx + xdy = 036.A bucket of water of mass 20 kg is pulled at constant velocity upto a platform 40 meters above the ground. This takes 10 minutes,during which time 5 kg of water drips out at a steady rate througha hole in the bottom. Find the work needed to raise the bucket tothe platform.B.8660 JD. 6680 Jx+4yf(x)=x2−4x−2