2. Consider two spheres of equations r² + y² + z² = 2x - 2y + 4z-2 and x² + y² + ² = 4x+2y+4. (a) For which points P on the first sphere and Q on the second sphere is the distance d(P.Q) maximum? (b) Find the volume of the solid that lies inside both of the above spheres. (Hint: First show that in a sphere of radius R the volume of a spherical cap (or spherical dome) of hight h is V = = ™h² (3R – h).)

Q: (c) Consider the parallelepiped with sides: u=(5,-2,1), v=(3,2, 4), and w=(-6,1,1). V (i) Find the…

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Q: 4. A 3D solid has base that sits in the x-y coordinate plane. That base is a triangle with vertices…

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Q: 4. Find the volume of solid G bounded above the cone z = √3√x² + y² and below the sphere x² + y² +…

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Q: 2. Suppose you revolved the triangular region bound by the axes and the line 4x + 3y = 12 completely…

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Q: 6 (A) 2x-yS6 (B) 2+y<6 (C) 2-y26 (D) +2y26

A: The solution are next step

Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

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Q: Write down inequalities to represent (a) the region inside the sphere 2² + y² + 2² = 62 and outside…

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Q: d the volume and the dinata plonac and on

A: Given the surface                   z=10-2x-y2

Q: 6. Using Second Theorem of Pappus, calculate the volume of solid of revolution when the area of the…

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Q: Find the AREA and VOLUME (Identify what type of volume) bounded by the equations; y = 4x - x² and x…

A: The given curves are y=4x-x2 and x+y=4 We have to find the area and the volume bounded by these…

Q: Consider two spheres of equations x² + y² + x² = 2x - 2y + 4z -2 and x² + y² + z² = 4x+2y+4. (a) For…

A: Given, x^2+y^2+z^2=2x-2y+4z-2 and x^2+y^2+z^2=4x+2y+4 Now we have to solve the following problem.

Q: 4. Find the surface area of the part of the sphere x² + y² + z² = 1 above the plane z = 1/√2.

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Q: 3. What is the equation of a circle that has a diameter of 16 units if its center is at (-2,-6)?

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Q: 12. Determine the volume of the solid above the surface z = √x² + y² and inside the sphere x² + y² +…

A: The given problem is to find the volume of solid bounded above by cone and bounded inside the…

Q: 2 1.² + a² 6² 1² Find the area enclosed by the ellipse x² that the area common to ellipse a² b² 2…

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Q: 6. Show that the area of the triangle intercepted from the co ordinate axes by the tangent to the…

A: We have to show that the area of the triangle intercepted from the coordinate axes by the tangent to…

Q: Find the surface area of the part of the sphere x² + y² + z² = 4 that lies above the cone z = √√x² +…

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Q: The space with lower border the parbolic 2: xy and upper border the level 2=4, must be divi ded into…

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