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- Find the exact volume of the solid that results when the region bounded in quadrant I by the axes and the lines x=9 and y=5 revolved about the a x-axis b y-axis5. Give formulas for the volume and the surface area of acylinder whose radius r is half of its height h.3.Calculate the volume of the rotating object that occurs if the area in the first quadrant is bounded by the curve x = y2 + 1, the X axis, the line y = 1, and is rotated around the Y axis
- for the region bounded by y=3x, the x-axis, and x=1, determine which of the following is greater: the volume of the solid generated when the region is revolved about the x-axis or about the y-axis. when the region is revolved about the x-axis, the volume is ? when the region is revolved about the y-axis, the volume is ? Which volume is greater?1. Find the area bounded by the curve y = x^2 and the x-axis and the ordinates x = 0 and x = 2 2. Find the volume generated by revolving the first quadrant area bounded by the parabola y^2 = 4x and x = 3 about the x-axis?3. Give formulas for the volume and the surface area of acylinder with radius y and height s.
- Given that the area R is limited by the curve y = x + 1, y = −x + 1 and the line y = α, 0 ≤ α ≤ 1. Determine the constant α, such that the volume of the rotating object that occurs when the area R is rotated about the x-axis equals 2π / 3 unit volume1)Sketch the solid obtained by rotating the region bound byy=2√x and y=x, about the line x =−2. 2)Write the expression for the area of a representative washer 3)Set up and solve the definite integral used to calculate the volume of the solid in (1)Given a curve having an equation of y2 = 4x. a) Compute the area bounded by the curve and the line y = 4 and x = 0.b) How far is the centroid of the curve bounded by the line y = 4 and x = 0 from the x-axis.c) What is the volume generated by this curve if it is revolved about the x-axis.
- Given: The region is bounded by the curve y=4x-x^2, y=4 and the y-axisProblem : The volume generated by the region bounded by the given curves rotated about y - axis is shown below. Find a + b. V= a/b pie cu. unitsSuppose that a cylindrical can is designed to have a radius of 1 in. and a height of 5 in., but that the radius and height are off by the amounts dr = +0.03 and dh = -0.1. Estimate the resulting absolute change in the volume of the can.1) Use the cylindrical shells to find the volume of the solid obtained by rotating the region bounded by y=x2, y=0, and x=6, about the y-axis 2) Use the cylindrical shells to find the volume of the solid obtained by rotating the region bounded on the right by the graph of g(y)=3/y and on the left by the y-axis for 1<y<9, about the x-axis. (Round nearest hundredth)