A right prism has height h and bases that are regular hexagons with sides s. Show that the volume is s'hV3.

Q: The base of a pyramid is a regular hexagon with sides y cmlong. The lateral edges are 2y cm long.…

A: The base area of the pyramid is the area of a regular hexagon with a side length of y cm.  So the…

Q: A conical tank that is 5 meters high has a radius of 2 meters, and is filled with a liquid that…

A: Inverted cone Now, put the origin of the coordinate system at the center of the top of the tank,…

Q: A right circular cone has a slant height of 12 ft and a lateral area of 967 ft'. Find its volume.

A: Given slant height and lateral area of cone are 12 ft and 96πft2, respectively. Obtain radius of the…

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: A solid has a circular base of radius 3. What is the volume of the solid if vertical cross-sections…

A:

Q: Determine the height of the right circular cylinder of greatest volume that can be inscribed inside…

A: It is given that,  Radius of cone is, R=4 in Height of cone is, H=12 in   Let semi vertical angle is…

Q: what is the volume generated if the area bounded by the cirves x2 =8y , x=4 and y= 0 is resolved…

A:

Q: Calculate the volume generated by the circle x^2 + y^2 -4x=-3 that revolves around ox

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Q: Find the volume of the solid whose base is an isosceles triangle (with base 6 meters and sides 5…

A: Given a solid whose base is an isosceles triangle (with base 6 meters and sides 5 meters) and whose…

Q: calculate the volume of the 1st octant under the plan 2x + y + z = 10

A: answer

Q: Given the area in the first quadrant bounded by the curve x2 = 8y, the line x = 4 and the x – axis.…

A:

Q: Two identical spheres are placed so that one is on top of the other inside a right circular cylinder…

A: This question is related to cylinders and spheres, we will solve it using given information.

Q: Find the volume of the solid whose base is the semicircle y = /25 – x² where –5 < x < 5 and the…

A: Given the base of the solidy=25-x2 , y&gt;0The intersection of the base with the x-axis :Put y =…

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: Find the volume of the solid whose base is a circle with radius 12 that has cross-sections…

A: Recall that the volume of a solid, if the cross-section is perpendicularto the x axis, and its area…

Q: A cone is formed from a circular piece of material of radius 1 meter by removing a section of angle…

A:

Q: Find the volume of the largest right circular cone that can be inserted in a sphere of radius 3.

A: The volume of the cone is given by  , where is the radius of the circular base of the cone and h is…

Q: A solid has a circular base of radius 3. What is the volume of the solid if vertical cross-sections…

A:

Q: Find the volume of the solid whose base is bounded by the circle x2 + y? = 36 and whose cross…

A: Given query is to find the volume of the give solid.

Q: The line segment from (0,0) to (5,20) is revolved about the x-axis to form a cone. What is the…

A: First find equation of line then Use formula of volume

Q: Get the volume of solid of revolution. Using Circular Disk Method.

A:

Q: A 120° sector is cut out of a circular piece of tin with radius 6 in. and bentto form the lateral…

A: Given: A 120° sector is cut out of a circular piece of tin with radius 6 in i.e., cone's slant…

Q: What is the volume in the first octant bounded by x2 = 16 – y and z + y = 16.

A: Given curves are

Q: What is the volume obtained by revolving the are biunded between the lines y=x, y=2x and x=4   about…

A:

Q: Find the volume (in m3)  of a right truncated triangular prism with a triangular base whose sides…

A: Please follow step 2nd .

Q: Find the volume of a right spherical segment of 2 bases if the radius of the sphere is 10 in.; the…

A: To find the volume of a right spherical segment of 2 bases. If the radius of the sphere is 10…

Q: Find the height of a right circular cylinder of maximum volume, which can be inscribe in a sphere od…

A: Topic:- geometry

Q: A cylindrical drill with radius 4 is used to bore a hole through the center of a sphere of radius 9.…

A: Given that:                    Radius of drill, r=4Radius of spher, R=9

Q: Find the dimensions of a right cone with surface area S=4 n that has the largest volume?

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the volume generated by revolving the plane area generated by the equations y = ex^2, y=0, and…

A: To find the volume of solid formed when the region bounded by y=e-x2, y=0 and  x=0  about the…

Q: Find the volume of the largest right circular cylinder that can be cut from a circular cone of…

A:

Q: Find the volume enclosed by the torusp = 4 sin().-

A: The volume is given by: V=∫∫∫dv In spherical co-ordinate dV=ρ2sin φ dρ dφ dθ

Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose…

A:

Q: Find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius…

A:

Q: The axes of two circular cylinders of radius a intersect at right angles. Show that the volume…

A: 8∫0ady∫0a2-y2dx∫0a2-y2dz = 8∫0ady∫0a2-y2dx (a2-y2)8∫0ady∫0a2-y2dx∫0a2-y2dz  =8∫0ady…

Q: Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 2.

A: Volume of the cone is given by 13πr2h, here r is the radius of cone (and not the sphere), h is…

Q: Find the volume of the torus obtained by revolving the circle x^2 + y^2 = 4 about the line x = 3.

A: Find the volume of the torus obtained by revolving the circle x^2 + y^2 = 4 about the line x = 3.

Q: A cone is formed from a circular piece of material of radius 1 meter by removing a section of angle…

A: To determine the largest possible volume for the cone, if a cone is formed from a circular piece of…

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

A:

Q: Derive the equation for the volume of a sphere of radius r using the shell method.

A: Consider a circle of radius (r), which when rotated around x-axis generates a sphere.

Q: A sphere with radius r is inscribed in a cylinder. Find the volumeof the cylinder in terms of r.

A: let a right circular cylinder of radius 'R' and height 'H' is inscribed in the sphere of the given…

Q: A cylindral drill with radius 5 cm is used to bore a hole through the center of a sphere with radius…

A: We are drilling the cylindrical hole through the centre of the sphere. So the height of cylindrical…

Q: Find the volume obtained when the circle of radius 1 withcenter (1, 0) is rotated about the y-axis.

A: We have to find volume obtained when the circle of radius 1 with center (1,0) is rotated about the…

Q: A right prism has height x and bases that are equilateral triangles with sides x. Show that the…

A: Given, A right prism has height x and bases that are equilateral triangles with sides x.

Q: Find the exact volume of the solid of revolution that results when a rectangular region with…

A: Given data: When the rectangle is rotated about its length then the revolution gives the right…

Q: Engr Thomas Pendot wants to construct a frustum from a right circular cone. At what distance from…

A: Let h be the distance from the base of the right circular cone which also the height of the frustum.…

Q: Two identical spheres are placed so that one is on top of the other inside a right circular cylinder…

A: topic - volume of cylinder

Q: Find the volume of the portion of the solid sphere ps8 that lies between the cones o= and ф %3D 3 3…

A: The portion of the solid sphere ρ≤8 that lies in between the cones ϕ=π3  and  ϕ=2π3

Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose…

A:

Q: A ball of radius 12 has a round hole of radius 5 drilled through its center. Find the volume of the…

A: let the resulting volume of solid is Vr  Vr = 6452.83 detailed solution is given below