Exam 14: Section 5: Multiple Integration

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Find the area of the surface for the portion of the paraboloid Find the area of the surface for the portion of the paraboloid   in the first octant. in the first octant.

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A

A company produces a spherical object of radius 17 centimeters. A hole of radius 7 centimeters is drilled through the center of the object. Find the volume of the object.

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Find the area of the portion of the surface Find the area of the portion of the surface   that lies above the triangular region with vertices   , and   . that lies above the triangular region with vertices Find the area of the portion of the surface   that lies above the triangular region with vertices   , and   . , and Find the area of the portion of the surface   that lies above the triangular region with vertices   , and   . .

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Set up a double integral that gives the area of the surface on the graph of Set up a double integral that gives the area of the surface on the graph of   over the region   . over the region Set up a double integral that gives the area of the surface on the graph of   over the region   . .

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Find the area of the surface given by Find the area of the surface given by   over the region R.    over the region R. Find the area of the surface given by   over the region R.    Find the area of the surface given by   over the region R.

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Find the area of the portion of the surface Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places. that lies above the region Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places. . Round your answer to two decimal places.

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Find the area of the surface for the portion of the sphere Find the area of the surface for the portion of the sphere   inside the cylinder   . inside the cylinder Find the area of the surface for the portion of the sphere   inside the cylinder   . .

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Find the area of the portion of the surface Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places. that lies above the region Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places. . Round your answer to two decimal places.

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Find the area of the surface given by Find the area of the surface given by   over the region R.   R: square with vertices  over the region R. Find the area of the surface given by   over the region R.   R: square with vertices  R: square with vertices Find the area of the surface given by   over the region R.   R: square with vertices

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Find the area of the surface given by Find the area of the surface given by   over the region R.   R: rectangle with vertices  over the region R. Find the area of the surface given by   over the region R.   R: rectangle with vertices  R: rectangle with vertices Find the area of the surface given by   over the region R.   R: rectangle with vertices

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Write a double integral that represents the surface area of Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places. over the region R: Write a double integral that represents the surface area of   over the region R:   . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places. . Use a computer algebra system to evaluate the double integral. Round your answer to four decimal places.

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A company produces a spherical object of radius 24 centimeters. A hole of radius 5 centimeters is drilled through the center of the object. Find the outer surface area of the object.

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Set up a double integral that gives the area of the surface of the graph of f over the region R. Set up a double integral that gives the area of the surface of the graph of f over the region R.    Set up a double integral that gives the area of the surface of the graph of f over the region R.

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Find the area of the portion of the surface Find the area of the portion of the surface   that lies above the region   . that lies above the region Find the area of the portion of the surface   that lies above the region   . .

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Set up a double integral that gives the area of the surface of the graph of f over the region R. Set up a double integral that gives the area of the surface of the graph of f over the region R.    Set up a double integral that gives the area of the surface of the graph of f over the region R.

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Find the area of the portion of the surface Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places. that lies above the region Find the area of the portion of the surface   that lies above the region   . Round your answer to two decimal places. . Round your answer to two decimal places.

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Find the area of the surface of the portion of the plane Find the area of the surface of the portion of the plane   in the first octant. in the first octant.

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Write a double integral that represents the surface area of Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places. over the region R: triangle with vertices Write a double integral that represents the surface area of   over the region R: triangle with vertices   . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places. . Use a computer algebra system to evaluate the double integral. Round your answer to two decimal places.

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