Find the volume of the right-circular cylinder using slicing, given that its base has a radius of 2 units with a height of 5 units. The center of one of the bases of the cylinder is at the origin.

Q: Find the volume of the solid that lies in the first octant I

A: In this question, we find the volume of solid bounded by sphere, coordinates planes, and the cone.…

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

A: given x-112+y2=1 claim- to find the volume of torus generated by revolving the region bounded by the…

Q: Find the volume of the solid S whose base is the disk bounded by the circle x^2 + y^2 = r^2 and the…

A: Solution is given below:

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

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Q: What is a correct set-up for finding the volume of the pyramid bounded by the coordinate planes and…

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

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Q: Find the volume of the solid whose base is given by 9. whose cross-sections perpendicular to the…

A: We will first find the area of cross section. Then integration of Area will be required volume of…

Q: Find the volume generate by rotating the given region about the specified line. R2 about BC

A: Integrating a small volume element within appropriate limits will result in the complete volume of…

Q: Find the volume of the solid bounded by the planes given below

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Q: Find the volume of the solid whose base is the semicircle y = √9 - x² where -3 ≤ x ≤ 3, and the…

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Q: Find the volume of a solid where the base of the solid is  a circle with radius 2, and the cross…

A: Let the circle be centered at origin and the radius is 2.

Q: Use disk, washer, or shell method to compute the exact volume obtained by rotating the region…

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Q: Derive the formula for the volume of a sphere of radius r by slicing.

A: We have, a sphere of radius r. The differential element shown in the figure is cylindrical with…

Q: Use the general slicing method to find the volume of the following solid. The solid with a…

A: According to General Slicing Method: Suppose a solid object extends from x=a to x=b and the…

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

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

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Q: Find the volume and the surface area of a “closed boOx' that has dimensions of 15 cm, 20 cm, and…

A: Given that: The dimensions of a " closed box" are 15 cm , 20 cm and 0.25m. 1m = 100 cm

Q: Use the shell method to find the volume of the following solid. A right circular cone of radius 3…

A: Consider the given information.radius is 3 and height is 8.The volune of right circular cone is…

Q: For a right circular cylinder, suppose that r = 6 in and H - 7 in. Find the exact:Total area,…

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Q: The cube is 3cm on one edge. Each of these joints A and B is 1cm from the vertex nearest it. If two…

A: This question is based on 3-D volume calculation in whivh two plane cut a wedge from a cube. We got…

Q: Use disk, washer, or shell method to compute the exact volume obtained by rotating the region…

A: In this question, we have given the region bounded by the curves f(x)=3x-14 g(x)=6-x and x=0. Here…

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: Find the volume of the figure with base bounded by the given curves such that slices perpendicular…

A: To find- Find the volume of the figure with base bounded by the curves such that slices…

Q: Find the volume of the solid that results when the region enclosed by the given curves is revolved…

A: Given: y=2cosx, With a=π4 , b=π2about x axis. Using disk method: V=∫abπr2dx

Q: Consider a right-circular cylinder of diameter 1. Form a wedge by making one slice parallel to the…

A: The diameter of the right circular cylinder is d=1. The angle which is made by other slide to the…

Q: Find the volume generated by rotating the region bounded by y = x, x = 1, and y? = 4x, about the…

A: Given curves are y=x, x=1   and  y2=4x We have to calculate the volume generated by these curves…

Q: Find the Volume enclosed by N = x2+y² and

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Q: Use the Theorem of Pappus to find the volume of the solid that is generated when the region enclosed…

A: y = 8−x² given y = x²     given This means that 8- x² = x² 2x2=8 x=-2,+2 Then, y=4,4

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Find the volume of the region cut from the solid sphere ρ≤ a by the half-planes θ = 0 and θ = π/6 in…

A: Find the volume of the region cut from the solid sphere.

Q: Use the disk method to verify that the volume of a right circular cone is 1/3 πr2 h, where r is the…

A: Given that: verify that the volume of a right circular cone is 1/3 πr2 h, where r is the radius of…

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

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

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Q: find the volume aquired by taking by region bound by  y=x^2 and  y=x^4 and rotating it around x=-1

A: To calculate the volume bounded by the curve y=x2 and y=x4 which is rotating about the line x=-1.…

Q: Find the volume of the solid whose base is the triangle enclosed by y-axis, y = 3, and y above…

A: First draw the base of the solid and find the cross section area then integrate.

Q: Which is closest to the volume of the space in the package that is not occupied by the ball?

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Q: Show how to use the shell method to derive the formula for the volume of a right circular cone with…

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Q: Find the volume of the following tetrahedron: z)|0<x<2(1-z), 0<y<3| 1 T =

A: Given that  The region of the tetrahedron is  To fidn the volume of the tetrahedron is

Q: Find the volume generated by revolving the area bounded by the parabola x2 = 4y and its latus rectum…

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Q: Find the volume of the solid of revolution bounded by the circle +y = 16, and the lines 0 and

A: To find: Volume of the solid

Q: Given the region bounded by y= x^3 ,x = 2, and the x-axis (in Quadrant I) is rotated about the line…

A: Given problem:- Given the region bounded by y=x3 ,X = 2, and the x-axis (in Quadrant I) is rotated…

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

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Q: Find the volume of the solid whose base is the region enclosed by y=x^2 and y=1, and the cross…

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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: Use the Theorem of Pappus to find the exact volume of a general cone created by rotating a triangle…

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.