Chapter 8.3, Problem 9E

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.

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)

Find the volume generated by revolving the regionbounded by y=−x^4+3x^3, y=0  revolving about the x − axis. Show the element of area on the grid provided.

The base of a solid is the region enclosed by the circle x^2 + y^2 =9. Cross-sections perpendicular to the x-axis are isosceles right triangles with the hypotenuse in the base. Find the volume of the solid.

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 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.

Find the centroid of the triangle bounded by the x-axis, the y-axis, and the line 2x + y = 5. The centroid is at | Note: Enter your answer as an ordered pair, e.g., (5,7). Now find the volume of the solid obtained by revolving the above triangle about the line x = 7. Volume is