= 1, 三 a NIU + +

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: Let V be the volume of a pyramid of height 20 whose base is a square with side length 8.

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Q: Find the volume of the solid cut from the cylinder x? + y? = 100 by the planes z = O and a + z = 7.

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Q: Find the volume of the solid obtained by rotating the triangle with the vertices A(0,0), B(4,4) and…

A: Solution

Q: The base of a solid is the region bounded by the ellipse 4x2 + 9y? = 36. Find the volume of the…

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Q: Determine the larger volume. Assume there is a hemisphere which has a radius of 5cm was cut by a…

A: A sphere of radius 5. V = Volume of hemi-sphereV = ∫02π∫0π2∫05r2sinθdrdθdϕ r : radial distance from…

Q: Find the volume of the described solid A frustum of a pyramid with square base of side b  ,…

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Q: Find the volume of the solid that lies inside both the cylinder a? + y? = 1 and the sphere 2? + 3? +…

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Q: Find the volume of the by 2j + i, i – j, and k.

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Q: Use the Theorem of Pappus to find the volume of thegiven solid.A cone with height h and base radius…

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Q: Find the volume of this cone.

A: we have to find the volume of the given cone.Given : radius of cone =11 mheight of the cone : 27 m

Q: The sides of the base of a regular octagonal pyramid is 8 cm. The angle between the lateral edges…

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Q: Find the volume of the ball x2+y2+z2≤R2.

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Q: Find the real number b such that the volume of solid B (r, +

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

A: We need to evaluate volume.

Q: Find the volume of the solid that lies under the elliptical paraboloid z = 2x? + y + 4 and above the…

A: V=∫∫RzdA V=∫01∫012x2+y2+4dydx Integrate with respect to y, V=∫012x2y+y33+y01dx…

Q: Find the volume of the pyramid with base in the plane z=−5 and sides formed by the three planes y=0…

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Q: Find the volume of the and the coordinate planes. tetrahedron bounded by 2x-y +z = 4

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Q: Choose the best coordinate system to find the volume of the portion of the solid sphere ps3 that…

A: Using spherical coordinate.

Q: Find the volume of the pyramid with base in the plane z = and sides formed by the three planes y -9…

A: To solve the following problem

Q: The volume of the tetrahedron bounded by the coordinate planes and the plane x+y+z=4 is

A: Given

Q: Find the volume of the largest closed rectangular box in the first octant having three faces in the…

A: To Find: Volume of the largest closed rectangular box in the first octant having three faces in the…

Q: Determine the volume generated by revolving the plane figures about y axis. 4m 3m 1m 2m 4m 2m

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Q: Find the volume of the oblique circular cylinder. The axis meets the plane of the base to form a 45°…

A: To find the volume of the oblique circular cylinder. The axis meets the plane of the base to form a…

Q: Find the volume of the torus generated by revolving the circle (x - 2)2 + y2 = 1 about the y-axis.

A: To determine the volume of the torus generated by revolving the circle.

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: Find the total area and volume of a rectangular solid with dimensions 8,6, and 5

A: Consider the given dimension as, l=8, b=6 and h=5

Q: Find the volume of the region enclosed by the paraboloid (x-1)²+y? =z and the plane 2x+z=2.

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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: The volume of the sphere with the radius 3 is = _ cubic units %3D 547

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Q: Determine the volume generated by revolving the plane figures about line a-a. a y 3m 2m 2m 2m 2m 2m…

A: ----------------------------------------------------------------------------- Equation of line…

Q: The volume of the sphere with the radius 8 is = cubic units 1024T 3 5127 3 2048T 3 30727 3

A: The formula for volume of sphere is given by: V=43πr3 Where r is the radius of sphere. Here r=8

Q: Find the volume of the torus (donut) with radii r and R as shown in the figure.

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Q: Choose the formula for the volume of a sphere of radius r.(a) 4/3 πr 2 (b) 4/3 πr 3 (c) 4πr 3 (d)…

A: The volume of a sphere of radius r is,

Q: The edges at a common vertex of a tetrahedron are perpendicular to each other. The lenghts of these…

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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 the region enclosed by the cone z = x² + y² and the sphere r2 + y? + z² = 4.

A: Solve for volume

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

A: Please see the attachment

Q: %3D y = 4-2r %3D D R.

A: Since, the prism is - D=x,y,z0≤x≤2,0≤y≤4-2x,0≤z≤6or0≤x≤4-y2,0≤y≤4,0≤z≤6

Q: Calculate the volume of the given solid. The tetrahedron enclosed by the coordinate planes and the…

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

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: Find the volume of the solid that lies under the elliptical paraboloid z = 2x2 + y? +4 and above the…

A: Given, z=2x2+y2+4 To find Volume of Solid

Q: For the right triangular prism, suppose that the sides of the triangular base measure 4 m, 5 m, and…

A: a) The measure of the triangular base is 4 m, 5 m and 6 m and the altitude is 7 m. The lateral area…

Q: Find the volume of the solid cut from the cylinder a? + y? = 100 by the planes z = 0 and a + z = 7.…

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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: The volume of the tetrahedron bounded by the plane * ++ = :1, {a, b, c > 0} and the coordinate a…

A: Volume of the figure will be given by integral - V = ∫∫∫dzdydxLet's find limits of z,y and x - Given…

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.