Use spherical coordinates to find the volume of a ball with radius R(in other words, use spherical coordinates to prove the volume formula V =4πR^3/3)

Q: use cylindrical coordinates. Find the volume of the solid that lies within both the cylinder…

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Q: In cartesian coordinate system, differential volume element is dxdydz. Infer the differential volume…

A: Concept:

Q: A cylindrical tank of radius 5m and height 18 m that tank two third filled with Liquid (Liquid asity…

A: Follow the procedure given below.

Q: Two spherical tanks are connected as in the figure below. The first tank has the radius 1m and is on…

A: Given, radius of first tank= 1 m radius of second tank= 0.5 m bottom of second tank is 2 m above the…

Q: A car on an amusement park ride travels in a circular path at a speedof 4.0 m/s. If the radius of…

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Q: ^2) and

A: In this question, the concept of Spherical Coordinates is applied. The Cartesian Coordinate system…

Q: The volume of the solid obtained by rotating the region enclosed by x=0, y=1, x=y^5   Whats the…

A: According to the given information, it is required to determine the volume of the solid by rotating…

Q: Please help me with question 5. I don't know how to find the volume of the solid region when it is…

A: Given, y=e0.5x and y=x2 intersecting at x=b To find the volume of the solid when the region is…

Q: Find the moment of inertia of the solid formed by revolving about ox the area bounded by a^2y=x^3,…

A: The given problem is to find the moment of inertia of the solid formed by revolving about an x-axis…

Q: differential

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Q: Find the volume cm^3 of the solid figure in Fig 1182 that was generated by rotating the shaded…

A: Volume of revolution

Q: Find the dimensions of a cylindrical can with a volume of 560 in^3 that minimizes the surface area.…

A: Let the radius of the cylindrical can be:  r Let the height of the cylindrical can be:  h

Q: What is the Volume between two equal regions between 3d curvatures?

A: Integrals and derivatives are considered as the inverses of each other. For example if we have a…

Q: 6.2.2 To be able to find the center of gravity, the center of mass, and the centroid of a composite…

A: For figure 1 :The composite body consists of a semicircle, circle, rectangle, and triangle assuming…

Q: M is solid cylinder centered on z-axis. Radius 7 and bounded by planes z=-4 and z=-8. Density of M…

A: Given information: M is solid cylinder centered on z-axis. Radius 7 and bounded by planes z=-4 and…

Q: In the figure shown, a 0.5-m by 0.5-m square plate had a semicircular hole of radius 0.25-m punched…

A: Given that Here we need to find the moment of the area of the plate. For that, we need to find the…

Q: Please use cylindrical coordinates to derive the formula for the volume of the ellipsoid 2 (~²)² +…

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Q: Explain why triple integrals that represent the volumes of solids are sometimes easier to evaluate…

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