Find the centroid of the lateral surface of a solid cone of base radius a and height h (cone surface minus the base).

Q: Use spherical coordinates to find the volume of the solid. 2 Solid inside x² + y² y² + z² = 9,…

A: The spherical co-ordinate from a rectangular co-ordinate s given as, z=r cosϕx=rsinϕcosθy=rsinϕsinθ…

Q: Find the moment of inertia about the z-axis of a solid of constant density δ = 1 that is bounded…

A: Given:

Q: Find the coordinates of the center of mass of a planar lamina bounded by the curves y = x and x = y.

A: find explanation below

Q: Determine the location of the centroid of the solid formed by revolving about the y-axis, the area…

A:

Q: with a 200 mm q

A: answer is in next step

Q: 2. x = 9-y?, y-axis; about x =9

A: Volume of the curve about x=9

Q: use spherical coordinates to find the volume of the solid. Solid inside x2 + y2 + z2 = 9, outside z…

A:

Q: Determine the centroid of the solid generated by revolving the area bounded by the curve y = x2, y=…

A: Given: The following figure is drawn for the given curve and a line.

Q: Find the volume and centroid generated by revolving the given plane area about the indicated axis: x…

A:

Q: find the centroid of volume if the volum is equal to 7/15 π

A:

Q: Find the centroid (center of mass) of the following thin plate, assuming constant density. Sketch…

A:

Q: Determine the location of the centroid of the solid formed by revolving about the y- axis, the area…

A:

Q: The boundary of a lamina consists of the semicircles y = V4 - x2 and y = V 36 - x2 together with the…

A: The semicircles are y=4-x2  and y=36-x2

Q: use spherical coordinates to find the center of mass of the solid of uniform density . Solid lying…

A:

Q: Find the lateral surface area of the cone generated by revolving the line segment y = x/6, 0 sx s2…

A:

Q: Find the centroid of a homogeneous half-ball of radius R.

A:

Q: Find the volume of the solid bounded by the elliptic paraboloid z = 1+ 2x² + 5y², the planes * = 5…

A:

Q: Use cylindrical coordinates to find the volume of a sphere of radius a from which a central cylinder…

A: The equation for the sphere in cylindrical coordinate system is r2+z2=a2. where, b ≤ r ≤ a and…

Q: Find the centroid of the solid generated by revolving about the indicated axis the area bounded by…

A: Given y2=x, y=3, x=0, about the y axis.

Q: Calculate the volume of a solid on the first octant and under the plane defined by 2x+6y+6z=24.…

A: Let's find.

Q: Use spherical coordinates to find the volume of the solid. Solid inside x2 + y2 + z2 = 81, outside z…

A:

Q: Use spherical coordinates to find the center of mass of the solid of uniform density. Hemispherical…

A:

Q: Find the centroid of the area of a trapezoid that has two equal slanting sides, a 6 cm base and a 3…

A:

Q: Find the volume of the solid bounded by the plane z = 10 - 5x - 8y and the coordinate planes in the…

A:

Q: Find the volumes of the solids obtained by rotating the region bounded by the following curves about…

A:

Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabolas y = 2x2 and y…

A: Given,

Q: Find the volumes of the solids obtained by rotating theregion bounded by the curves  y= x and  y =…

A: Note: As you are not mentioning about which axis, so we are solving about x-axis. For another axis…

Q: 5. x=9-y', x-y-7= 0 about x = 4

A:

Q: 4. y= 6x- x', y = x? - 2x, y = -1

A: We find the volume.

Q: Find the center of mass of solid revolution if an area in Ist Quadrant (Kuadran Pertama) bounded by…

A: Given functions are Intersection points Area of region is Centre of mass revolution

Q: Find the Surface Area of the solid generated by revolting the solid bounded by y=2√x, y=0, x=3,…

A: The Surface Area of the solid generated is given by,

Q: 9. y=1-x2, y = 0, x=1, x 2; about x = 1

A: Here is the solution

Q: Find the moment of inertia about the x-axis of a thin plate of constant density d covering the…

A:

Q: Determine the area and the centroid (x,y) of the area.

A:

Q: 11. y = x, x =0, y = 5; about x-axis

A: Here is the solution

Q: Find the centroid of the lamina enclosed by y = v1 – x2 and above X-axis. Assume that the density of…

A:

Q: Find the centroid of the lateral surface of a solid cone of base radius a and height h (cone surface…

A:

Q: Locate the centroid (x¯,y¯) of the area.

A: The area is bounded by the curves:fx=3-112x2 ; y=3 ; x=6

Q: 3. y = 4x, y = 2x – 4; about y-axis

A: Here we find volume.

Q: use spherical coordinates to find the moment of inertia about the z-axis of the solid of uniform…

A:

Q: 8. y = x', x=0, y = 8; about y = 8

A:

Q: Use spherical coordinates to find the volume of the solid. Solid inside x + y- + z² = 81, outside z…

A: To find the volume of the solid inside the sphere x2+y2+z2=81 and outside the cone z=x2+y2, and…

Q: use spherical coordinates to find the moment of inertia about the z-axis of the solid of uniform…

A:

Q: Use Pappus’s Theorem for surface area and the fact that the sur-face area of a sphere of radius a is…

A:

Q: Find the volume of the solid bounded by the plane z = 3 - 5x - 9y and the coordinate planes in the…

A:

Q: Find the centroid of a thin flat plate covering the region enclosed by the parabolas y = 2x and y =…

A: Solution of question is written in step2 and step3.

Q: Use cylindrical coordinates to find the volume of the solid region bounded on the top by the…

A:

Q: 12. y = x', x =0, y= 3, (first quadrant); about x-axis

A: Given that, y = x2,    x = 0 and y = 3 We have to find the volume generated by revolving the given…

Q: Locate the coordinates of the centroid/center of gravity X

A: concept: First we have to find equation of given Circle of radius r. With the help of given Circle…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.