Definition: The median center of a solid S is the point (c, Cy, C) with the following property:• Half the mass of S lies on one side of the plane r = C;• Half the mass of S lies on one side of the plane y = Cy:• Half the mass of S lies on one side of the plane z = c,.That is, the planes r = C,, y = Cy, 2 = c; each divide the solid into two parts of equal mass.In two dimensions, the coordinates of the the median center of a plate (cz, Gy) have the property that the linesx = C, and y = cy each divide the plate into two parts of equal mass.Note that the median center is not the same thing as the center of mass!12.For the solid of density 6(r, y, 2) = 2 +1 occupying the region enclosed below the sphere r? +y? + 2? = 16 and above the cone z = V + y², find the median center (c, Cy, Cz).

The solid stands at the origin and is divided by x = 0 and y = 0. 16-r2 As the density increases…

Answered: 12. For the solid of density 6(r, y, 2)…

12. For the solid of density 6(r, y, 2) = z +1 occupying the region enclosed below the sphere r?+ y? + 22 = 16 and above the cone z = VP +y², find the median center (, Cy, C).

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter10: Measurement, Area, And Volume

Section10.6: Surface Areas Of Pyramids And Cones

Problem 27E

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Question

Definition: The median center of a solid S is the point (c, Cy, C) with the following property:
• Half the mass of S lies on one side of the plane r = C;
• Half the mass of S lies on one side of the plane y = Cy:
• Half the mass of S lies on one side of the plane z = c,.
That is, the planes r = C,, y = Cy, 2 = c; each divide the solid into two parts of equal mass.
In two dimensions, the coordinates of the the median center of a plate (cz, Gy) have the property that the lines
x = C, and y = cy each divide the plate into two parts of equal mass.
Note that the median center is not the same thing as the center of mass!
12.
For the solid of density 6(r, y, 2) = 2 +1 occupying the region enclosed below the sphere r? +
y? + 2? = 16 and above the cone z = V + y², find the median center (c, Cy, Cz).

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