1. Find the volume of the solid bounded by the paraboloids 2 = r2 + 3y²...
Find the volume of the solid bounded by the paraboloids z = - 9+ x2 + y2 and 2 = 7 – 22 – y? Round the answer to the nearest whole number.
(5) (a) (4 points) Sketch the solid E bounded by the paraboloids z = 3.+ 3y² and z = 4-22 - y". Also find and sketch the projection of the solid E onto the cy-plane. (b) (6 points) Find the volume of the solid E from part (a).
Find the volume of the solid bounded by the elliptic paraboloids
and
2= 12 + 5y 2 = 24 – 5.2 - 4
15. Use a triple integral to find the volume of the solid enclosed between the paraboloids 3x2 +y2 and z 8-x2-y2. z
15. Use a triple integral to find the volume of the solid enclosed between the paraboloids 3x2 +y2 and z 8-x2-y2. z
Find the volume of the solid bounded by the cylinder x2 + y2 = 1, and the planes 2x + 3y + 2z = 7 and 2 = 0 (Note: Remember to type pi for 7. Also keep fractions, for example write 1/2 not 0.5.) V= M
Problem 8. (1 point) Find the volume of the solid enclosed by the paraboloids 2 = 16 (? + y) and 2 = 18 - 16 (2? + y).
1. Find the volume of the solid generated by rotating the region bounded by yı = 2.c and y2 = Vt around the x-axis. 2. Find the volume of the solid generated by rotating the region bounded by y = r? and y2 = x around the y-axis.
1. Find the volume of the solid created by revolving the region bounded by the curves y = r2 and 2.2 + y2 = 1 about the 2-axis. 2. A spherical tank has a radius of 8 m. If the tank is completely filled with water, compute the work required to pump all of the water to the level of the top of the tank.
Find the volume of the given solid region bounded below by the cone z = \x² + y2 and bounded above by the sphere x2 + y2 + z2 = 8, using triple integrals. (0,0,18) 5) 1 x? +y? +22=8 2-\x?+y? The volume of the solid is (Type an exact answer, using a as needed.)
please answer 1&2
Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y = 5x", y = 5x, x2 0; about the x-axis V = Sketch the region. y у 5- 6 4 3 3 N -0. 0.5 1.0 X 1.5 -0.5 0.5 1.0 1.5 Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line. y2 =...