Find the volume of the solid cut from the first octant by the surfacez = 4 - x2 - y.

Q: Determine the volume of the solid formed when the region enclosed by the curve y = √x, x -axis and…

A: Given regions are y=x, y=0 and x=4.

Q: Draw the area bounded by function y = x^2 + 1 and line y = 5, then calculate the volume of the solid…

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Q: Find the volume of the solid generated by revolving the region by graph of function f(x) 10 ;x 1.25,…

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Q: Find the volume of the solid obtained by rotating the region bounded by y= 54x-6x2 and y= 0 about…

A: Given:           y=54x−6x2 and y=0  about y−axis.

Q: Find the volume formed by revolving about the line y = 2a, the area bounded by that line, the curve…

A: As per rule of Barbtleby we can solve only one question at a time and we can solve only three…

Q: Find the volume of the shaded region about the indicated axis. y =x (1, 1) y = Vr+2 -2

A: Find the volume we use the disc method for first picture and cylindrical shel method for second…

Q: Find the volume of a cone generated by revolving about the y-axis the area bounded by the line…

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Q: Find the volume of the solid whose base is the semicircle y = √9 - x² where -3 ≤ x ≤ 3, and the…

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Q: Find the volume of the solid formed by rotating the region enclosed by y = x3 and y = 4x in the…

A: We first sketch the region using a graphing calculator  y=x3 (blue) y=4x (green) The shaded region…

Q: Find the volume of the solid of revolution formed when the area of the region bounded by y3Dx2,…

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Q: Find the volume of the solid generated by revolving the region between y = 4 – x2 and y = -x + 2…

A: The given regions are, y=4-x2 and y=-x+2 and the given line is, x=44-x=0 We can write the given…

Q: Find the volume of the solid formed by rotating the region enclosed by y=x3and y=4x in the first…

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Q: calculate the volume of the 1st octant under the plan 2x + y + z = 10

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Q: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 16 and whose cross…

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Q: Find the volume of the solid of revolution formed by rotating the area under y=9-x2 over [0, 3]…

A: Given curve is y=9-x2 ,[0,3]

Q: Evaluate the volume of the surface of the shaped recreated by revolving the line y = 1/x as x goes…

A: Solution is written in below steps.

Q: Find the volume of the solid whose base is the semicircle y = /25 – x² where –5 < x < 5 and the…

A: Given the base of the solidy=25-x2 , y&gt;0The intersection of the base with the x-axis :Put y =…

Q: Find the volume of a right circular cone with height 18 and base radius 9 using integration.

A: Take a cross-section area of thickness dx at a distance x from top, integrate it from 0 to 18.

Q: Find the volume of the solid generated by revolving about the x-axis, the area bounded by y = x3,…

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Q: y = 9x² and y = 0 about x = −4

A: Given:        y=9-x2 and y=0         x2=9           x=3 about x=-4

Q: Find the volume in the first octant between z=9-x^2-y^2 and the cylinder x^2+y^2=1.

A: The given surfaces can be plotted as follows: Thus, the required solid will be R=x, y, z: 0≤x≤1,…

Q: Find the volume of the solid whose base is in the first and second quadrant(s) bounded by y = 32 –…

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Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About…

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Q: Find the volume of the solid formed by invoving the region by the graphs y=x^3 , y = 0 , x = 1 ,…

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Q: Find the volume of the solid generated by revolving the region bounded by the y = x2 and y=6x-2x2…

A: Given that y = x2 and y = 6x- 2x2 and we find volume about the y-axis and plot the graph. Here i…

Q: Find the volume of the solid cut from the first octant by the surface z=4-x2-y.

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Q: Find the volume of a solid extending from y = 2 to y = 5 if every cross section has area A(y) = 5.

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Q: . Find the volume of the solid whose base is the region bounded by the semicircle y = 1– x² and the…

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Q: Find the volume of the solid formed by revolving the region bounded by the graphs of the equations…

A: The volume made by full revolution of area between the curves y1=f1(x) and y2=f2(x) where y2&gt;y1…

Q: Determine the volume of the solid formed by revolving the area bounded by y= X² and x=y² about the…

A: The formula for the volume of the solid formed by revolving the region bounded by the curves, y=f(x)…

Q: find the volume of the solid obtained by rotating the region enclosed by the graphs aboutthe given…

A: We graph the region using a graphing calculator. Red is y=16-2x Blue is y=6 The shaded region is…

Q: What is the volume generated when the area bounded by y=2x2+1; x=1; x=2 is revolved about the line…

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Q: Find the volume of the solid generated by revolving the region bounded by the graph 1 4x -x4, the y-…

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Q: Find the volume when the area in y = 2x^2 − 8x + 12 and y = −2x + 12 is 9 sq units and revolves…

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Q: Find the volume of the solid of revolution generated by revolving y = 9-x from x= - 3 to x= 3 about…

A: Given f(x)= 9-x2    where -3≤x≤3 To find the volume of the solid of revolution here use The Disc…

Q: Find the volume of the region bounded above by the surfacez=9- y2 and below by the rectangle R:…

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Q: Find the volume formed by rotating the region enclosed by: y = x³ + 1, the y-axis, and y = 9 about…

A: We will use the disk method to evaluate the volume of the solid of revolution.

Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

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Q: Find the volume of the solid. y=9-x2, y=0, about the x-axis

A: The given solid is bounded between the curve y=9-x2, y=0,  rotating about the x-axis. Volume of the…

Q: Find the volume of the solid generated when the region enclosed by y = sqrt(2x + 8), y = x, x = 0 is…

A: Given :     To find the volume of the solid.

Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose…

A: According to the given information it is required to find the dimension of right circular cylinder…

Q: Find the volume of the solid generated by revolving the shaded region about the y-axis. y 3

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Q: Compute the volume of the solid obtained by revolving the graph of the function f(x)= 9x5 on the…

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Q: Find the volume of the solid formed by rotating the region between the y=sqrt(x)curve  y=2 line and…

A: The volume of the solid of the revolution can be calculated using integration. The formula for the…

Q: Compute the volume of the solid obtained by revolving the graph of the function f(x) = 8x³ on the…

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Q: Find the volume of the solid formed by revolving the region bounded by the graphs of y=x^2+3 and…

A: The Washer Method : The volume of the solid generated by revolving about the x-axis a region between…