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Chapter 5: Q45P (page 248)

Find the mass of the solid in Problem 43 if the density is proportional to x.

Short Answer

Expert verified

The required Mass of the solid is4615K .

Step by step solution

01

Definition of Mass

A physical body'smassis the amount of matter it contains. It's also a measure of inertia, or the resistance to acceleration when a net force is applied.

02

Finding the Mass

Consider the density to be蚁=Kxandfind the value of the mass.

M=鈭�V蚁dV=K鈭�01xdx鈭�02xdy鈭�x2+y2+82x2+y2+12dz=K鈭�01xdx鈭�02xdyx2+4=K鈭�02x3+4xdx鈭�02xdy

Simplify and solve further.

M=K鈭�02x3+4xdx鈭�02xdy=2K鈭�01x4+4x2dx=2Kx55+43x301=215+43=4615K

Therefore, the required Mass of the solid is4615K .

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Most popular questions from this chapter

Verify that (3.10) gives the same result as (3.8).

For the solid bounded above by the sphere x2+y2+z2=4and below by a horizontal plane through (0, 0, 1), find

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