How do you find the volume of the solid bounded by the coordinate planes and the plane 6x + 5y + z = 6?

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Answer 1 · 2016-11-19T09:06:17

1.2 cubic units.

The plane meets axes at A(1, 0, 0), B(1, 6/5, 9) and C(0, 0, 6).

The intercepts OA = 1, OB = 6/5 and OC =6.

Use pyramid volume formula

Volume = 1/3(base area)(height).

The volume of the tetrahedron OABC

= 1/3 (area of the #triangleOAB) (OC)#

#=1/3(1/2(OA)(OB))(OC)#

= (1/6)(1) (6/5 )(6

=6/5 cubic units.