Chapter 8.3, Problem 8E

The radius length of the base of a right circular cylinder is 6 in. The height of the cylinder is 10 in. Find the exact a Lateral area b total area c volume.

Calculus revolve the area bounded by a pentagon with vertices (1,0), (2,2), (4,0),(-2,2),(-1,0) about the x- axis and find the volume generated. correct answer is 108.91 cubic units.

Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = x°, y = 1, x = 2; about y = -5 V = Sketch the region. y y 4 Sketch the solid and a typical disk or washer. Graph Graph Description Graph Graph Description Graph Graph Description Graph Graph Description 15- -2 --15 -15 ol

5) Find the volume of the solid generated by revolving the triangular region with vertices (0,0), (b,0), (0,h) about: a) x-axis ○ (bh^3/3)pi C. units. (bh^2/3)pi C. units. ○ (bh^3/2)pi C. units. (bh^2/2)pi C. units.

Please explain steps in details: Density of water is approximately 1000 kg/m^3 and gravity is 9.81 m/s^2 . The function y = x^2 from x = 0 to 2 is rotated about the y-axis. 1) Find the volume of the resulting solid 2) If the resulting solid is filled with water, find the work done in emptying it - assume all units of measurement are in meters. Do we subtract? 3) Find the surface area of the resulting shape (set up the integral, and find a numerical approximation)

Please sketch it and find the volume of solid correctly according to the question asked

Help me please

*Sketch all appropriate regions or solids.* Find the volume of the region Q bounded by z = 0 and f(x,y)= Ja² - (x² + y² ). Change from rectangular to spherical coordinates. You may give the answer without evaluating the volume of the solid Q. Sketch the solid Q.

Quiz/ Find the volume of the solid generated by revolving the region bounded by the parabola ( y? = 2x) and the line (y=x) about (a) the x- axis, ) the line x=3