. Find the volume of the curve bounded by y = 1/x, y = 2/x, and the lines x = 1 and x = 3 rotated 13 about the x-axis.

Q: Find the volume of the cap of a sphere of radius r and height h for h < r.

A: The equation of the sphere with radius r is x2+y2+z2=r2. Determine z2 from the equation of sphere.…

Q: 2. Refer to the figure and find the volume obtained by rotating the given region about the specified…

A: a) Given that, the radius r=1-x4 and the region is lies between a=0 and b=1. Obtain the area of  the…

Q: 1. Show that the volume ofa parallelepiped with sides A. B and C given by A (B x C)

A: As per our guidelines we are supposed to solve only one question i.e. the question no 1. For the…

Q: Let B be the solid whose base is the circle (x^2) + (y^2) = (4^2)  and whose vertical cross sections…

A: This question is based on application of Integration.

Q: ® Eualuate the inteyral- ... taken. throughout the volume o f sphere b=2+

A: To evaluate ∫∫∫1a2-x2-y2-z2dx dy dz Taken throughout the volume of sphere x2+y2+z2=a2

Q: A sphere of radius r is cut by a plane h units above the equator, where h &lt; r. Find the volume of…

A:

Q: Use the Theorem of Pappus to find the volume of the solid of revolution. the torus formed by…

A:

Q: 5. Use the Pappus Theorem to find the volume of the solid formed by revolving the region enclosed by…

A: In this we find the volume of the solid by using pappus theorm.

Q: Prove that the volume of a segment of height h of a sphere of radius r is V = }nh°(3r – h)

A:

Q: Find the volume obtained by rotating R about the line = -e.

A: Volume : π2e2+4e+1

Q: Find the volume of the torus generated by revolving the region bounded by the graph of the circle…

A:

Q: If the region enclosed by the y-axis, the line y=2 and the curve y=sqrtx is revolved about the…

A: Proceed as shown below...

Q: Compute the volume lying inside the sphere x2 + y? + z2 = 46 but outside of x² + y? = 21.

A:

Q: Determine the volume generated by revolving the plane figures about y axis. 4m 3m 1m 2m 4m 2m

A:

Q: Given the area in the first quadrant bound by x^2= 8y m, the line x=3 and the x-axis. What is the…

A:

Q: Find the volume generated by revolving about the x-axis, the area bounded by the line 2x + 4y = 4,…

A: I am attaching image so that you understand each and every step.

Q: Find the volume of the region in the first octant enclosed by the cylinder x^2 +y^2 =4 and the plane…

A:

Q: Find the volume generated by revolving the area enclosed by the curve x? + y? = 16 about ne y-axis.

A:

Q: Show by integration that the volume of a sphere of radius r is V=4/3 πr³

A:

Q: Find the volume of the solid formed when the region bounded by the curve y? = x, the line y = 1 and…

A: Definite integrals can be used to compute areas and volumes of solids of revolution. Cylindrical…

Q: The region in the first quadrant bounded by x2 + y? = 1, x = 2, and y = 1 is revolved about: 1- The…

A:

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: Given data:     The given function is: y=2(x)1/4. The given limits of y is: [a,b]=[0,2].   The given…

Q: Find the volume generated by rotating the given region about the specified line. R, about BC

A: In this question, we find the volume by rotating the region R1 about the line BC.

Q: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the…

A: Sphere was cut at height h, radius of the circle at intersection of 2 cuts is r2-h2. Similarly…

Q: Use the Theorem of Pappus to find the volume of the solid of revolution. the torus formed by…

A: We have to use theorem of pappus to find the volume of solid of revolution The torus formed by…

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: The given figure is,

Q: Use washers to find the volume formed by rotating the region enclosed by: y = 1.6 – 0.2|x – 11| and…

A:

Q: Determine the volume generated by revolving the plane figures about line a-a. a y 3m 2m 2m 2m 2m 2m…

A: ----------------------------------------------------------------------------- Equation of line…

Q: Refer to the figure and find the volume generated by rotating the given region about the specified…

A: Here, the line OB is y=4x. So the shell radius is 1-x and the height is 4x.

Q: use the disk method to find the volume (in units^3) when the regionbounded by the curves x+y=5, x=0,…

A:

Q: 1. Use the cylindrical shells to find the volume of the solids generated when the shaded area is…

A: The volume of solid of revolution can be calculated using the cylindrical elements. The formula for…

Q: A torus is generated by rotating the circle x2 + (y – R)² = r² about the x-axis. Find the volume…

A:

Q: Compute the volume of the solid above the cone o = , and between the spheres p = 1 and p = 3. Hint:…

A: We have to use spherical co ordinate system

Q: Find the volume of a sphere. 4/3piR^3 using cylindrical shells

A:

Q: If a plane region R located in the first quadrant is revolved about the x-axis, then the measure of…

A: False.

Q: Find the volume.

A:

Q: Find the volume of the solid bounded by a lune with an area of 36t. The given angle is 25°. C D Q..…

A: To Find: the volume of spherical wedge bounded by lune with an area of 36π, and an angle of 25°.

Q: Use the disk method to verify that the volume of a right circular cone is (1/3)π r2h, where r is the…

A:

Q: 3. Use the method of Exercise 2 to find the formula for the volume of a right circular cone of…

A:

Q: 6. Find the volume of the torus generated by revolving the circle x² + y² = 4 about the line .x = 3.

A:

Q: Find the volume of the cap of a sphere with radius R and height h using a triple integral. R.

A: Consider the following figure By Pythagorean theorem x2+y2=R2 ⇒x2=R2−y2

Q: A torus is formed by revolving the region bounded by the circle x2 + y2 = r2 about the line x = R,…

A:

Q: Use the Washer Method to find the volume obtained by rotating the region in Figure 3 about the…

A:

Q: Compute the volume lying inside the sphere x? + y? + z? = 37 but outside of x² + y? = 21.

A:

Q: Calculate the volume of the region bounded by the sphere a2 + y? + z? = 5 from above and by the cone…

A:

Q: 1. Use Pappus' Theorem to find the volume V of the torus generated by revolving a circular region of…

A: There are two Theorem by Pappus 1st for surface area of revolution and 2nd for volume of revolution…

Q: If we have a half-circle of radius r centered at 0, prove thatthe volume of the sphere resulting…

A:

Q: Let a sphere of radius r be cut by a plane, thereby forming a segment of height h. Show that the…

A:

Q: 9. Find the volume generated by revolving the given plane area about the given line using the disc…

A: We are given two regions: (a) y=2x2, y=0, x=0, x=5 about x-axis. (b) x2-y2=16, y=0, x=8 about…

Q: Use the theorem of Pappus to find the volume of a torus (pictured here). Assume that a disk of…

A: We know by the theorem of Pappu that the volume of a solid is obtained by area times the distance…