45. Find the volume of the solid in the first octant bounded by the cylinders x² + y² = a², x² + z² = a². %3D

Q: 2. Find the volume generated by revolving about the y-axis, the area bounded by x² + y² = a² and x+y…

A: The bounded region: Green colored    To find: The volume of revolution around y-axis of the bounded…

Q: Find the volume of the solid obtained by rotating the region bounded by x = 2 – y? and x = y about…

A: Consider the given functions. x=2-y2 and x=y Put both the functions equal.…

Q: 7. Find the volume of the solid obtained by rotating the region under the graph of f (x) = 9 – x2…

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Q: 9. Find the volume of the solid whose base is the region enclosed by y = 2 –- x² and the x-axis and…

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Q: 2. Find the volume of the solid generated when the region bounded by y = x2 - x and y = x- x2 is…

A: First of all for calculating the volume of the solid revolving around any particular axis, graph…

Q: 3 14. Find the volume of the solid that results when the region bound by y = x°, x = 2 and the…

A: The given region is the region bounded by y=x3,x-axis y=0 and x=2. To find the volume when the…

Q: The volume of the solid formed by rotating the region bounded by y = 6/(x^2) and the x-axis from x =…

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Q: Find the volume of the region between the cylinders x² + y² = 36 and x? + z2 = 36.

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Q: 2. Find the volume of the solid generated when the region bounded by y = x? - x and y = x – x² is…

A: For calculating the volume of the solid revolution about particular axis, we will find the original…

Q: 8 Use the method of cylinders to determine the volume of the solid obtained by rotating the region…

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Q: Compute the volume cut out of x2 + y2 + z2 = 64 by the cylinder x2 + y2 = 64.

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Q: Find the volume of the region that is between x = 8 – z2 – y? and x = -V4y² + 4z²

A: b)the region bounded by surface x=8-y2-z2andx=-4y2+4z2inside the disky2+z2=4

Q: Find the volume of the solid obtained by rotating the region bounded by x = -6+ y² and a y about the…

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Q: 11. Find the volume of the a 3-dimensional solid whose base is given below and whose cross sections…

A: TO FIND THE VOLUME OF SOLID GIVEN BELOW FORMED BY THE CURVES  y=4-x2 ; y=0 ;x=0 by using the concept…

Q: 12. Find the volume of the solid that results when the region bound by x 1-y and the y-axis is…

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Q: 5. Find the volume of the solid in the first octant bounded by the two cylinders x²+y²=4 and…

A: I am attaching image so that you understand each and every step.

Q: 31. Use the trapezoidal rule with n= 7 to estimate the volume of the solid generated by rotating the…

A: We know that; The expression for the volume of the revolution about the x-axis is: V=∫abπy2dx Given:…

Q: What is the volume of the solid whose 1 30 cross-sections are squares perpendicular to the x-axis…

A: Given: The region bounded by the curves are: y=x and y=x The cross-sections are squares…

Q: 22 Find the Volume of the Solid of revolution bound al by the circuit x*+y=16, aud the lineSX=0 and…

A: Equation of the circle is given as x2 +y2 = 16 x2 +y2 = 42 Where radius of the circle r is 4 unit…

Q: 2.5 Find the volume of the solid of revolution formed by rotating the area under y = 9 – x? over [0,…

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Q: 4. Find the volume of the region bounded by y = -x+1, x = 0 and y = 0 revolved about the x-axis.

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Q: 4.Find the volume of the solid that is obtained by rotating the region bounded by y = /x +1, y = Vx…

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Q: 10. Find, among all right circular cylinders of fixed volume V, the one with smallest surface area…

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Q: What is the volume in the first octant bounded by x² + y – 4 = 0 and z = x. Use a triangular…

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Q: 14 - Which of the following is the volume of the object that occurs when the region bound by the y=…

A: We sketch the region using a graphing calculator  The shaded region will rotate around the x axis

Q: What is the exact volume of a solid that is formed by rotating the region bounded by g (x) = †x² +1,…

A:

Q: Define Q as the region bounded by the functions f(x)=x^2/9 and x=2 in the first quadrant between y=2…

A: Use the washer's method to solve the problem. The volume of the solid is given by V=π∫cdfy2-gy2dy.

Q: What is the exact volume of a solid that is formed by rotating the region ,2 bound by g (x) = x + 4,…

A:

Q: What is the exact volume of a solid that is formed by rotating the region bounded by g (x) = †x²+1,…

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Q: 4. Compute the volume rotating the area shown through one revolution about the x-axis. generated by

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Q: 4. Find the volume of the region bounded by y = - x+1, x = 0 and y = 0 revolved about the x-axis.

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Q: 3-Find the volume of the solid obtained by rotating the region bounded by y=2x+1, x=4 and y=3 about…

A: .

Q: 3. Find the volume of the solid formed by y = √√4sin(x) bounded by x = 0 revolved about the x axis…

A: According to the question we need to find out the volume of revolution of the curve.

Q: Find the volume between the cylinders x+y =1 and the cylinder x* +z* = 1 in the first octant. 2

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Q: 4. Set up a (sum of) definite integral(s) that is equal to the volume of the solid whose base is R…

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Q: 6. Find the volume of a solid whose base is the region bounded by y = 4 – x² and the x-axis and…

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Q: What is the volume in the first octant bounded by x2 = 16 – y and z + y = 16.

A: Given curves are

Q: 2) Find the volume generated by the area bounded by y = x², y = 4x, revolved about x-axis.

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Q: 2) ( ) Sketch and find the exact volume of the solid obtained by rotating the region B bounded by…

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Q: What is the volume in the first octant bounded by x2 + y − 4 = 0 and z = x. Use a triangular…

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Q: 3. Find the volume of the solid generated by revolving about the line x = 3 the region in y = 2x2 –…

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Q: Compute the volume bounded by y=x²-2x and 3y +2x²-27=0 when it is revolved around the y-axis

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Q: 9) Find the volume of the region bounded by y = x + 1 x +1' Y = 0, x = 0, and у %3D0, х%3D x = 4…

A: The formula for the washer method around the x-axis is V=π∫abf(x)2-g(x)2dx where f(x) is the top…

Q: 5. If the first cylinder is x + y = a², where a 1?

A:

Q: 2. Find the volume of the region common to the cylinders r2 + y² = 9 and z2 + z² = 9.

A: USING  FORMULA VOLUME =8∫∫∫dxdydz

Q: 18. Find the volume of the solid obtained by revolving the region under the graph of y = 5- on [1,…

A: To find the volume of the solid obtained by revolving the region under the below graph on [1, ∞)…

Q: 23. Find the volume of the solid formed by the region in the first quadrant bounded by: x = y-y3, x…

A: Consider the graph:

Q: Find the volume of the region bounded above by the paraboloid z = 3 - x2 - y2 and below by the…

A: Given: To Find: The volume of the region bounded above by z=3-x2-y2 and below by z=2x2+2y2.…

Q: 2. Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.