Find the surface area of a) The part of the plane 3x + 2y +z = 6 that lies in the first octant b) The part of z = xy that lies in the cylinder given by x? + y? = 1

Q: 4. Find the volume of the region bounded above by the paraboloid z = x? + y? and below by the…

A: (4) Consider the provided question, According to the provided question, draw the graph of the given…

Q: Find the volume V of the solid S that is bounded by the elliptic paraboloid 2.r2 + y? +z = 27, the…

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Q: Determine the larger volume. Assume there is a hemisphere which has a radius of 5cm was cut by a…

A: A sphere of radius 5. V = Volume of hemi-sphereV = ∫02π∫0π2∫05r2sinθdrdθdϕ r : radial distance from…

Q: The circular cross-section of the cylinder, y + z? = 4, can be obtained by cutting it along any…

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Q: B) Show that V=367 is the volume of a sphere of radius 3 by using spherical coordinates.

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Q: 9. Use spherical coordinates to find the volume of the part of the ballps 4 that lies between the…

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Q: What is the center of gravity of the solid formed when the plane region bounded by y = x^2 and y=x+2…

A: We sketch the given region using a graphing calculator as shown below:   The shaded region is…

Q: Compute the volume of the solid bounded by the hemisphere z = the horizontal plane z = c by using…

A: To compute the volume of the spherical cap, use the following formulae and convert the Cartesian…

Q: Find the "volume" of the four-dimensional pyramid bounded by w +x+ y+z-1=0 and the coordinate planes…

A: The volume of the four dimensional pyramid is given by, V=∫v1 dv   =∫dzdydxdw. The boundaries are…

Q: Evaluate the surface integral. ∫∫sxdS, S is the part of the plane 6x+3y+z=6 that lies in the first…

A: The plane has intercepts at (1,0,0), (0,2,0), (0,0,6). The parameterize the surface S by. where

Q: Compute the volume of the solidbounded by the paraboloid z =x+y and the upper hemi sphere 6 -x² -…

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Q: Use spherical coordinates to find the volume of the top half of the sphere x? + y? + z? = 4 that…

A: Given that a sphere x2+y2+z2=4 and a cone is z2=x2+y2 We have to find the volume of the top of the…

Q: Use spherical coordinates to find the volume of the solid enclosed by the sphere x2 + y² + z? = 4a?…

A: This question is about finding volume of solid enclosed by sphere. We can find it using triple…

Q: 9. Find the volume of the solid wedge cut from the first octant, bounded by the three coordinate…

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Q: The volume of the solid bounded by z = 0, x + y+ z = 4 and x? + y? = 4 in cylindrical coordinates is…

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Q: Find the volume of the solid bounded by the paraboloid z = 24 – x? = y?, the cylinder x2 +y² : 12…

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Q: Find the volume of the tetrahedron bounded by the four planes x=0,y=0,z=0, and 2x+2y+x=4?

A: The equation of the plane 2x+2y+z=4  can be rewritten in the form  z=4-2x-2y let z=0, 0=4-2x-2y…

Q: Find the volume of the solid bounded by the paraboloid z = 2 – 4x? – 4y? and the plane z =

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Q: Consider the paraboloid z = 1- ² – y?. Find the volume of the region between this surface and the ry…

A: According to the problem,. we have

Q: Find the volume of the solid bounded by the paraboloid z = 6x + 6y and the plane z = -

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Q: Find the volume of the solid enclosed between the cone z = hr? and the plane z = 2h.

A: The variables in cylindrical coordinate systems are r, z and θ. In this problem, we have to find the…

Q: 2. Use spherical coordinates to find the volume of solid within the sphere x² + y² +z? = 16 and…

A: we have to given equation of sphere is x2+y2+z2=16 and equation of cone is 3z2=x2+y2 we have to find…

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

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Q: Compute the volume of the solid bounded by the hemisphere z = √√4c² - x² - y² and the horizontal…

A: hemisphere z=4c2-x2-y2 and plane z=cTo Find: Compute the volume of the solid using spherical…

Q: Draw the solid of revolution obtained by rotating the given plane region about line L. Which figure…

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Q: Find the volume of the solid bounded by the paraboloid z = 28 – x? – y?, the cylinder x² + y? = 14…

A: To determine the triple integral,

Q: Determine the volume generated by revolving the plane figures about line a-a. a y 3m 2m 2m 2m 2m 2m…

A: ----------------------------------------------------------------------------- Equation of line…

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

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Q: Compute the volume of the solid bounded by the hemisphere z = = √4c² - x² - y² and the horizontal…

A: The given problem is to evaluate the volume of the solid bounded by given hemisphere z=√(4c2-x2-y2)…

Q: Determine the volume of the region that lies under the sphere x² + y² + z² = 4, above the plane z…

A: Given: Now,

Q: Find the volume of the solid bounded by the paraboloid z = 14 - 5x - 5y and the plane z=9 V= (Type…

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Q: The volume of the parallelepiped is Volume = |a x b||c|| sin | = |(a × %3D b). c| True False

A: Using direct formula

Q: Consider the area of the part of the plane z = ax + by+C that projects onto some region D in the…

A: If the area of the region D on xy-plane is k. That is, ∫∫DdA=k. If the area of the some region of…

Q: Interpret the volume below the surface z = x +y?, above the plane z = 0, and inside the cylinder x'…

A: The given problem is to find the volume of the region below the surface paraboloid z=x2+y2 above the…

Q: Calculate, by means of cylindrical or polar coordinates, the volume of the solid that is inferiorly…

A: we have to find out the volume of the solid which is bounded below by  z=2y and above by…

Q: Find the volume of the region enclosed by the cylinder x2 + y? x² + y? + 4. = 2, the plane z – x +y=…

A: We have to find the volume of the given region.

Q: Find the volume of the largest closed rectangular box in the first octant having three faces in the…

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Q: Find the volume bounded by the paraboloid z = 1+ 3x? + 3y? and the plane z = 16 in the first octant.

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Q: Find the volume of the solid that lies under the elliptic paraboloid z = 3y? – a? + 4and above the…

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Q: The volume of the parallelepiped is Volume = |a x b||c|| sin o| = |(a x b)- c| %3D %3D True False

A: We have to check either the volume of parallelepiped is volume=a×bcsinϕ=a×b·c or not.

Q: Write an integral formula of the solid generated by revolving the region enclosed by the triangle…

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Q: 9. Find the volume of the solid in the first octant enclosed by the surface z = x? and the four…

A: Volume = ∫02∫03∫0x2dx dy dz                 =∫02dx∫03dy ∫0x2dz…

Q: 9. Find the volume of the solid enclosed by the cone z = Vx? + y? and the plane z = 4.

A: we have to find the volume of the solid

Q: In Exercises 8-11, a region of the Cartesian plane is shaded. Use the Disk/Washer Method to find the…

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Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder r? + y? 64 and…

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Q: use the Causs theorem to reduce the surface integral (JA.ds) on all six faces of a cube whose volume…

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Q: Find the volume of the solid bounded by the elliptic paraboloid z = 5 + 4a² + 3y?, the planes a and…

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Q: Determine the volume of the solid lying under the elliptic paraboloid z = 6y? – 2x2 + 3 and above…

A: To evaluate the integral

Q: Compute the volume of the solid bounded by the hemisphere z = √4c²-x² - y² and the horizontal plane…

A: Here we will use spherical co ordinate to find volume of solid bounded between sphere and plane .…

Q: Find the volume V of the solid S that is bounded by the elliptic paraboloid 2.r² + y² + z= 27, the…

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