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

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

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

=6/5 cubic units.

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To find the volume of the solid bounded by the coordinate planes and the plane (6x + 5y + z = 6), you need to calculate the volume of the region enclosed by this plane and the coordinate planes.

This region is a tetrahedron, and its volume can be found using the formula for the volume of a tetrahedron, which is (V = \frac{1}{3} \times A_{base} \times h), where (A_{base}) is the area of the base of the tetrahedron and (h) is the height of the tetrahedron.

The base of the tetrahedron is a triangle formed by the intersections of the given plane with the coordinate axes. To find the coordinates of these points, set two of the variables to zero and solve for the third variable.

For (x = 0), (y = 0), and (z = 0), we get the points ((0, 0, 0)), ((0, 0, 6)), and ((1, 0, 0)) respectively.

Calculate the area of this triangle using the formula for the area of a triangle given its vertices.

Then, find the height of the tetrahedron, which is the perpendicular distance from the fourth vertex to the plane (6x + 5y + z = 6). This distance can be calculated using the formula for the distance from a point to a plane.

Once you have the area of the base and the height, plug these values into the formula for the volume of a tetrahedron to find the volume of the solid.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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