* Q. (41), p.305 : Find the volume of the solid generated of revolving V3 1 y V1 + x2 SxS V3 3 < x s %3D X

Q: 3. Find the exact value of surface area of the solid that is described by the intersection of the…

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Q: Find the volume of the solid bounded by the - 3+ 2x2 + 2y? and paraboloids z = z = 5 – x2 – y? -

A: To find the volume of the solid bounded by, z=-3+2x2+2y2 and z=5-x2-y2

Q: Let R be the region in the first quadrant bounded by the graphs of x = y and x=4y (a) Which is…

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Q: 2. Find the volume of the solid lying under the elliptic x2 paraboloid + 4 y2 +z = 1 and above the…

A: The elliptic paraboloid can be expressed as z=f(x,y) where fx,y=1-x24-y29. We have to notice that…

Q: 2) Find the volume of the solid bounded by the cylinder x2 + y = 16 and from z = 1 to z + x %3D 2…

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Q: The volume of the solid under the plane 4 x+ 5 y - z=0 and above the region enclosed 27 by y= 3 x…

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Q: ex: Evaluate SS (&++y²)dV over the first octont region boundeol by the cylinders x*ty=/ and xay=4…

A: Convert coordinate system into cylinder coordinate system. Sketch region D and find range of…

Q: iii. Find the volume of the solid bounded by z = 4 – x² – y in the first octant.

A: To find the volume of the solid

Q: In the given question , use the shell method to find the volume of the solid generated by revolving…

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Q: Find the volume of the given solid. Bounded by the cylinders x2 + y² = 4r2, y2 + z² = 4r2

A: We need to find the volume of given solid bounded by two cylinders x2+y2=4r2 and y2+z2=4r2

Q: The solid bounded by the surfaces S1,S2,S3,S4 and S5 corresponds to  image 1  If V is the volume…

A: We will use basic knowledge of triple integral and integral calculus to answer this question.

Q: THE REGION BOUNDED BY 2y = x AND (x-2)² = − 4y + 12 15 REVOLVED ABOUT THE LINE Y = 4. DETERMINE THE…

A: Introduction: The washer method refers to this application of the slicing method. Because the slice…

Q: - Find the volume of the solid generated by revolving about the line x = 1 the region bounded by the…

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Q: Q5) Find volume of body bounded by z2 + y2 + x2 = 4.

A: Given equation is z2 + y2 + x2 = 4

Q: Find the volume of the solid in R' bounde y = x², x = y² , z = x + y + 33, and z V =

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Q: 45. Find the volume of the solid in the first octant bounded by the cylinders x² + y² = a², x² + z²…

A: First we will calculate the volume common to both the cylinders.  Parallel area perpendicular to x-…

Q: Find the volume of the solid under the paraboloid z = 4–x²–y² and over the region x²+y² < 1.

A: We have to find the volume of the solid.

Q: D. 48. Find the volume of the solid obtained by rotating the region bounded by y = 3Vx and x = 4…

A: First, we sketch the region using a graphing calculator. The shaded region will rotate about the…

Q: 4. Find the volume of the solid obtained by rotating about y ax[is the re[gion between y=x^2 and…

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and…

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Q: What is the volume of solid of revolution between the curves y=x+1 andy 0 around the x-axis on…

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Q: 12. Find the volume of the solid bounded by the cylinder r2 + y² = 4 and the planes z = 0 and %3D y+…

A: The bounds are 0≤z≤3-y, -4-x2≤y≤4-x2 and -2≤x≤2.

Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

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Q: What is the volume of the solid formed by revolving the region bounded by the graphs of x2 = 7y and…

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Q: Q4. Find the volume of the solid that is bounded above by the surface z =1– 2x² – y? – 2y and below…

A: Step:-1 Volume V=∭dxdydz ----(1) Now, given that required region is bounded by surface z=1-2x2-y2-2y…

Q: Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-…

A: There are three methods to find the volume of a solid generated by revolving a curve f(x) about a…

Q: Find the volume of the solid below the cone z = /x² + y² and above the ring 1 < x² + y² < 4

A: The given solid lies below the cone z=x2+y2 and above the ring 1≤x2+y2≤4

Q: 12) Find the volume of the solid bounded by x² +y² = 4 and z=x+y in the first octant.

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Q: Which of the following represents the volume of the solid generated by revolving the region bounded…

A: the line y=x-1and y=(x-1)3 intersect in the points (0,-1),(1,0) and (2,1) the line y=x-1 is below…

Q: Find the volume.

A: Consider the provided question,

Q: The volume of the solid E bounded by the cylinder x +y = 4, and the planes z = 1 and z = 2 in the…

A: The Given volume of the solid can be found using the triple integral and converting the rectangular…

Q: - The region bounded by 2y = x and (x − 2)² = −4y + 12 is revolved about the line y = 4. Determine…

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Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)=x²+2x+…

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Q: 5. Find the volume under the paraboloid z = -x² – y², and above the cone z = -. -V#²+ y².

A: Given

Q: 6. Calculate the volume of the solid Q bounded above by x² + y? + z² – 2z = 0 and below by z = x² +…

A: We need to calculate the volume of the solid that is bounded above by x2 + y2 + z2 - 2z = 0 and z =…

Q: Find the volume of the solid formed by revolving the region bounded by y = sin x and the x-axis from…

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Q: Find the volume of the given solid. Under the surface z = 1 + x²y2 and above the region enclosed by…

A: To find the volume of the given solid.

Q: Example 16. Find the volume of the region D enclosed by the surfaces z = x² + 3y² and z = 8 – x2 -…

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Q: D Evaluate the volume of the solid region E, in the first octant, that lies above z0 and below the…

A: Explanation of the answer is as follows

Q: - Find the volume of the solid that is bounded above by the cylinder z = 4-x2, on the sides by the…

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Q: 3. Find the volume of the solid that lies under the paraboloid 5z = x² + y², above the xy-plane, and…

A: To find the volume of the solid that is bounded by given curves.

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)= x² + 2x…

A: Using disc method, volume is evaluated.

Q: 1. Find the volume under the parabolic f(x,y) = x²+ 4y² and above the rectangle R :0 < x < 1,1 < y <…

A: Given  fx,y=x2+4y2

Q: 5. Find the volume generated by revolving the area under the rve y = e² from r = 0 to x = 1 (a)…

A: y=e^x

Q: 1. Find the volume of the solid in the first octant bounded by the coordinate planes, the plane x =…

A: Note: Hi! Thank you for the question As per the honour code, We’ll answer the first question since…

Q: O Find the volume of solid in the first octant bounded by the co- ordinate planes, the planes x-3,…

A: We will find out the required volume of the solid in the first octant.

Q: Find the volume of the given solid. Under the surface z = 1 + x²y2 and above the region enclosed by…

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Q: 4 8. What is the volume of the solid generated when the region bounded by y= V4 +3x – x and y = 2 is…

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Q: Evaluate III Vx2 + y² dV E where E is the region that lies inside the cylinder x2 + y2 = 4 and…

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