Prove that if a sphere is inscribed in a right circular cylinder whose height is equal to the diameter of the sphere, then: 3 (a) The volume of the cylinder is the volume of the sphere. (b) The surface area of the cylinder, including its bases, is the surface area of the sphere. 3

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

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Q: show that :(A) the space of a cube is twice the surface of its diagonal. (B) The volume of a cube in…

A: Consider the lower base of a cube. Use Pythagorean Theorem in order to solve for the hypotenuse or…

Q: Let B be the solid whose base is the circle x^2+y^2=49 and whose vertical cross sections…

A: Given, Circle- x²+y²=49=7² --------equation 1 The equation is of the form x²+y²=r². Therefore, the…

Q: Use the Theorem of Pappus to find the volume of thegiven solid.52. A sphere of radius r

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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: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

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Q: Calculate the volume of the solid that is limited superiorly by the sphere x2+y2+z2=9 and inferiorly…

A: To Calculate: Volume of the solid bounded superiorly by x2+y2+z2=9 and inferiorly by x2+y2=z2.

Q: Use the disk method to verify that the volume of a sphere is 4/3 πr3 , where r is the radius ?

A: So sphere is basically a circle that is rotated through the x-axis. We will suppose to cut a disk…

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: 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)

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Q: Find the volume of the torus generated by revolving the circle (x - 2)^2 + y^2 = 1 about the y-axis.

A: Given: (x-2)2+y2=1

Q: 25. Find the volume of the solid that is enclosed by the cone z = /x² + y² and the sphere x² + y² +…

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Q: The base of a three-dimensional figure is bound by the line y = -2x + 5 on the interval [-1, 2].…

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Q: Find the volume of the solid that is enclosed by the cone  z = sqrt(x2 + y2) and the sphere  x2 +…

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

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Q: Use the Theorem of Pappus to find the exact volume of a general cone created vertices (0, 0), (1,0),…

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Q: Find the volume enclosed by the cy linder (x-1) ty²=1 and the sphere x² +y²7z²=L4.

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

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Q: Compute the volume lying inside the sphere x2 + y? + z2 = 35 but outside of x² + y? = 19.

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Q: Find the volume of the solid that is enclosed by the cone z = x² + y² and the sphere x² + y² + z² =…

A: Given: Equation of cone z=x2+y2 Equation of sphere x2+y2+z2=2

Q: Find the volume of the tetrahedron bounded by the four planes x=0,y=0,z=0, and 2x+2y+x=4?

A: The equation of the plane 2x+2y+z=4  can be rewritten in the form  z=4-2x-2y let z=0, 0=4-2x-2y…

Q: Show that (a) the total surface of the cube is twice the square of its diagonal, fo) the volume of…

A: Given- A cube with side s. To show- That Show that (a) the total surface of the cube is twice the…

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: Determine the volume of a four dimensional unit sphere: x, =r sin 8, sin 8, cos p, x, =r sin 0, sin…

A: The given problem is to find the volume of four dimensional unit sphere, we have to set up an…

Q: A rectangular box with a square base is inscribed in a right circular cone of height 4 and base…

A: Given:A rectangular box with a square base is inscribed in a right circular cone.The base radius of…

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: Use calculus to find the volume of a cap of a sphere with height h and radius r.

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Q: Determine the volume of the region that lies under the sphere x² + y² + z² = 4, above the plane z…

A: Given: Now,

Q: The volume of the sphere with the radius 8 is = cubic units 30727 3 512T 3 20487 3 10247 3

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

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

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Q: = 1, 三 a NIU + +

A: Here Let u = x/a, v = y/b , w = z/c Then dx = a du, dy = b dv, dz = c dw So, Required volume V =…

Q: 6. Use calculus to calculate and to prove that the volume of a right circular cylinder with radius r…

A: There are many ways to prove the volume of the right circular cylinder using calculus. The method of…

Q: Find the volume of the pyramid with base in the plane z = -1 and sides formed by the three planes y…

A: Please see the attachment

Q: Find the volume of the pyramid with the base in the plane z= -5 and the Sides formed by the three…

A: To find the volume of the pyramid

Q: Show that the surface area of a closed cuboid with square base and given volume is minimum , when it…

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: Find the volume of spherical segment of one base and altitude h cut from a  sphere of radius a.

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

A:

Q: The volume of the sphere with the radius 8 is = cubic units 30727 3 512T 3 2048T 10247T 3

A: To solve this we will use the formula of volume of sphere.

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: Find the volume of the solid that is enclosed by the cone z = and the sphere x² + y2 + z2 = 72.

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Q: Determine the volume of the largest rect an gu lar box in the first oct ant with three faces in the…

A: Given: The volume of the largest rectangular box is to be determined based on the first octant with…

Q: Show that the surface area of a closed cuboid with square base and given volume is minimum, when it…

A: Let the length be x , breadth be x and height be y of a closed cuboid with a square base.So Volume…

Q: Use the disk method to verify that the volume of a sphere is (4/3)π r3 , where r is the radius.

A: Volume of sphere of radius r is (4/3) πr3