Match the net with the corresponding solid. The corresponding solid to this net is a

Q: 7) z dV, E is the solid enclosed by the cylinder r2 +y = 1, and the E planes z = 0 and z 3.

A:

Q: Evaluate ||E y²z² dV, where E lies above the cone o and below the sphere p = 1. = T/3

A: Given, ∫∫∫Ey2z2dV   ....(i)Let x=ρsinϕcosθ y=ρsinϕsinθ and z=ρcosϕAnd we know…

Q: Evaluate ://| y} dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2,0, 0), (0, 2,0),…

A:

Q: A hollow frustum of a pyramid with following shape and main particulars floats in water: Psw=1.025…

A:

Q: For a right circular cylinder, suppose that r = 6 in and H - 7 in. Find the exact: a) L; b) T; c)…

A:

Q: The base of a solid is the region bounded by the x-axis and the graph of y V1-z. For the solid, each…

A:

Q: Question 15 Evaluate f S f6zdV E where E is the solid enclosed by z = 1 and z = x ² + y? O 27 47T…

A:

Q: W R X

A: →Centroid of a triangle is the point at which all three medians of triangle      intersect each…

Q: 7. In AVYX, the centroid is Z. Use the diagram to solve the problems. If VP = 51, find VZ and ZP.

A: We use the property ,the centroid divides each medians in the ratio 2:1.

Q: 6. Find the volumes of the solids in the following figure z =-VI - r?

A:

Q: A solid is constructed so that one side is the region between the lines z = a, x = b, the graph of y…

A: The cross-section of the solid are perpendicular to the x-axis and are isosceles right triangles so…

Q: Evaluate 3zdV E where E is the solid enclosed by z = 1 and z = x + y

A: we need to evaluate the given integral about the solid E . first we will find the limit of the…

Q: Verify Euler's formula for the solids below. (i)

A:

Q: Calculate the volume of the prisms with the following dimensions (refer to Figure 3.6): a = 4'0" a =…

A: Given: The dimensions of the prism A=1250 mm,  B=5950 mm,  h=3250 mm

Q: Find the Uolume of the Solid under de the 2:1+ xy2 & the a Gove te region Sorface en cased by y= x²…

A: Consider the given surface z=1+x2 y2 Since, y=1 and y=x2 Then, x=±1 That is, -1≤x≤1  and    x2≤y≤1

Q: The axis of symmetry of the cylinder is parallel to the z-axis. х-ахis. O y-axis.

A:

Q: y? dV, where T is the solid tetrahedron with vertices (0, 0, 0), (2, 0, 0), (0, 2, 0), and (0, 0, 2)

A: Given function f(x,y,z)=y2 Tetrahedron T is region with vertices (0,0,0), (2,0,0), (0,2,0) and…

Q: Evaluate / / /3zdV E where E is the solid enclosed by z = | and z = = x² + y?

A:

Q: What solid is formed when this net is folded? B D

A: there is no introduction for the above question.

Q: Oose the correct net for each solid shape. b) c) al b) al b) c) b) b) a) bi C)

A: We open these 3D figure and check the answer.

Q: The figure below shows the solid that lies under the paraboloid z = 5x? + 5y², and above the…

A: Given The solid lies under the paraboloid z=5x2+5y2 and above the XY plane, and inside the cylinder…

Q: 6. Evaluate (a + y) da dy dz, where D is the tetrahedron with vertices (0,0,0), (1,0, 0), (0, 1, 0)…

A: Introduction: The triple integral is applicable to find the volume of a solid enclosed by given…

Q: Find the volume of the given solid. Under the surface  z = 9xy  and above the triangle with…

A:

Q: If the density of the frame element (shown in the figure) is given as p(x, y)=b+cy where a-9, b-1.2…

A: Given  Density μx,y=b+cy Where a=9, b=1.2, and c=3.1

Q: If the region R = {(x, y) | x > 1, 0 < y < 1/x} is rotated about the x-axis, the volume of the…

A:

Q: Consider the solid Q that is generated in the first octant by the surfaces S1 : y+z = 4, S2 : y - 1…

A: Solution is below.

Q: V = LWH (volume of a rectangular solid) a. for W B. for H how would I go about getting W and H…

A: Explained below

Q: What is the region of the solid generated by the graphs of a = y – 4y and a = -y ?

A:

Q: 9. Find the surface area of the part of the paraboloid a = 2 – 2? – y? that lies inside the surface…

A:

Q: 1. Sketch carefully the solid enclosed by the three cylinders x + y* – 1,x² + 2² = 1, and y + z² =…

A:

Q: Find the volume of the given solid. Under the surface z = 6xy and above the triangle with vertices…

A: Given: z=6xy A triangle with vertices (1,1),(4,1),(1,2)

Q: 5. Evaluate y* dV, where E is the solid tetrahedron with vertices at (0,0,0), (2,0,0), (0, 2,0), and…

A: we can evaluate the given integral. ∫∫∫R f(x,y,z) dV =∫∫∫R f(x,y,z) dzdydx

Q: Evaluate the triple Integral. 3xyz dV, where T

A:

Q: 1. Evaluate I = D xy dA, where D is the triangular region with vertices (0,0), (0, 1), and (1,1).

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Consider the solid Q that is generated in the first octant by the surfaces S, : 2x + 3y + 3z = 6 S,:…

A: The region S2 is clearly a parabola y2 = 2-x and it is symmetrical in the x-axis.

Q: z dV, where E is the solid tetrahedron with vertices (0,0,0), (2,0,0), E Find (0,6,0), and (0,0,3)

A:

Q: If the region that lies inside the cardioid r = 1+ cos 0 and outside the cirele r = 1 is the base of…

A:

Q: If the density of the frame element (shown in the figure) is given as p(x, y)=b+cy where a=9, b=1.2…

A:

Q: Given: dyldx = (x^2 + y^2) / xy. What is the degree of the homogeneous DE? The given DE is not…

A: We have to solve

Q: Find the volume of the given solid. Under the paraboloid z = x² + 3y² and above the rectangle R= [0,…

A: Consider the provide question,

Q: Consider the solid generated by the surfaces octant the 1st in

A: The surfaces are given by x2+y2+z2=4   and y2+z2=2 To find the volume bounded by two surfaces in the…

Q: Find the volumes of the solids

A: We have,

Q: Evaluate y* dV, where E is the solid tetrahedron with vertices at (0,0,0), (2,0, 0), E (0, 2,0), and…

A:

Q: Which of the following is a solid of revolution? (a) Sphere (b) Pyramid (c) Cylinder (d) Cube

A:

Q: Consider the solid Q, in the first octant, which is generated by the surfaces: S1 : x2 = −(z − 3),…

A: Given:  S1 : x2 = −(z − 3), S2 : y + z = 3, S3 : z = 2, S4 : z = 0, S5 : y = 0 and S6 : x = 0  The…

Q: Sketch the solid given by the following constraints 1 ≤ r ≤2 0≤ θ≤π 0≤ z ≤2

A:

Q: 5xyz dv, where T is the solid tetrahedron with vertices (0, 0, 0), (1, 0, 0), (1, 1, 0), and (1, 0,…

A:

Q: Find z dV, where E is the solid tetrahedron with vertices (0,0,0), (5,0,0), (0,6,0), and (0,0,3)

A: This question is related to triple integral, We will solve it using given information.

Q: What solid is formed when this net is folded? A C D

A:

Q: The solid that is common to the interior below the hemisphere z = /80 – x² – y2 and above - the…

A: Set up a triple integral.

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.