Question 8 The base of a solid is the circle x? +y = 81. Find the volume of the solid given that the cross sections perpendicular to thex-axis are isoceles right triangles with leg on the xy-plane. a) O1948 b) O 1945 c) O1944 d) O 1947 e) O1946

Q: Find the area of the region enclosed by the graphs of: y? = 15 – x and x = 6. %3D

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Q: the volume of the indicated region. the region enclosed by the paraboloids z=x2+y2-2  and…

A: Given query is to find the volume generated by two curve.

Q: b) Find the volume of an inverted cone defined by: i. R< 2 and 0 <0 <"/3

A: the given question is taken from the calculus in which we have to find the volume of the cone so…

Q: 4.) Find the volume if the region enclosing y=x² and y=2x where x20 is rotated about the given line.…

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Q: 22) A sphere with r = 4 cm radius (a sphere) A) 67.0 cm2 B) 200.8 cm2 C) 267.9 cm2 D) 50.2 cm2

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Q: 3) Determine the shaded area shown in figure, (the shape is a regular hexagon with side length = 220…

A: Figure shows regular hexagon The triangle in hexagon is equilateral triangle . Area of equilateral…

Q: 1. Points A(2,1,0), B (4,1,6), C(5,3,s) and E (-8,5,t) are the vertices of a triangular prism where…

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Q: Q9) Find the volume V of the solid in the first octant whose graph on the right. a) V= c) V=2 b) V =…

A: Given that, the solid graph bounded by      We need to find the volume of the given solid.Limit of…

Q: - 1)? + (y + 2)? + (z – 4)? = 36 For the spheres (x and x? + y + z? a) surface areas. b) volumes.…

A: The generel sphere equation is x-a2+y-b2+z-c2=r2where a,b,c-centre and r-radius.Surface area of the…

Q: 6) A cylindrical can is to be made from wrapping 64 sq inches of rectangular sheet metal, Top and…

A: Use the reslut,For maximum volume of cylinder,            Height of cylinderRadius of cylinder = 2

Q: B) 53° D) 52° A) 88° C) 72° Find the value of x. 4) Determine the volume of the figure described.…

A: Apply intersecting chords theorem

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.