Use a triple integral in spherical coordinates to derive the volume of a sphere with radius a.

Q: a) Find the volume and the lateral surface area of the solid formed by rotating this func- tion…

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Q: The volume generated when ℝ is rotated about the x-axis.

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Q: y = cosx x = y = 0, x = 0

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Q: Express as an integral using spherical coordinates, then evaluate to find volume V for the region.

A: We need to find valoume of the given solid.

Q: z2 = 9 and outside the cylinder x? + y? = 1.

A: coordinates, x=r cos θy=r sin θz=2 x2+y2=r2cos2θ+sin2θ=r2x2+y2+z2=9r2+z2=9⇒z=±9-r2 x2+y2=r2⇒r=2

Q: Jse integration in spherical coordinates in order to obtain the general ormula for the volume of the…

A: To find the volume of the ball with radius R the volume of integral for the spherical coordination…

Q: Use cylindrical coordinates to find the volume of a sphere of radius a from which a central cylinder…

A: The equation for the sphere in cylindrical coordinate system is r2+z2=a2. where, b ≤ r ≤ a and…

Q: Write a triple integral in cartesian or spherical coordinates for the solid and solve for the volume

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Q: Sdlid inside x²+y?+2²=16outside

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Q: Let R be the region in the first quadrant bounded by the curves y = x³ and y = 2x – x² Compute the…

A: Volume about y-axis

Q: Let S be the solid enclosed by z = 6-√36 - x² - y² and x² + y² - 3z² = 0. a. Find the volume of S by…

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Q: b) y = x +1, y = x °+1 (in the first quadrant), about the x-axis. (method of shells)

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Q: Use cylindrical coordinates in order dervive the formula for the volume of the following ellipsoid:…

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Q: Find volume if area enclosed is rotated about y= -2.

A: To find the volume if the area enclosed by the below curves is rotated about y = -2.

Q: the region inside the solid sphere o ≤ 7 that lies between the cones A) 343 -TU 3 B) 343 6 T 343 4…

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Q: the region enclosed by the cone z² = x² + y² between the planes z = 4 and z = 10 A) 3127 D) 312 B)…

A: The region is enclosed by the cone z2=x2+y2 between the planes z=4 and z=10. We have to find the…