Question

Find the volume common to the cylinder x2+y2=a2 and x2+z2=a2.

Answer 1

x2+y2=a2
x2+z2=a2
_ _. _
(_2yz)

Answer 2

Answer:

16a^3/3 is the Answer

Step-by-step explanation:

Volume=8∫∫∫dxdxdydz=8∫∫∫a2−x2√z=0dxdydz=8∫∫(a2–x2−−−−−√)dxdy

Now in the XY plane we have a circle x2+y2=a2, y varies from 0 to a2−x2−−−−−−√ and x varies from 0 to a

V=8∫a0∫a2−x2√0a2−−√−x2dxdy=8∫a0[a2–x2−−−−−√.y]a2−x2√0dx=8∫a0(a2−x2)dx=8[a2x−x33]a0=8.2a^3/3=16a^3/3

The xy-plane is the plane which contains the x- and y-axes; the yz-plane contains y- and z-axes; the xz-plane contains x- and z-axes. These three coordinate planes divide the space into eight parts, which is known as octants. The first octant, in the foreground, is determined by the positive axes.

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