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Describe the cross section which is formed by the horizontal plane. Note that the figure is not drawn to scale. Use pencil and paper. Is it possible to have a horizontal cross section with different dimensions if you had the plane intersect the prism in another​ spot?

3 ft
6 ft
10 ft
Question content area bottom
Part 1
Which is the best description of the cross section of the rectangular​ prism?
A.
The cross section is a rectangle which has a different length but same width as the prism.
B.
The cross section is a rectangle which has the same length and width as the prism.
C.
The cross section is a square which has the same length and width as the prism.
D.
The cross section is a rectangle which has the same length but different width as the prism.

1 answer

To determine the correct description of the cross section formed by a horizontal plane intersecting a rectangular prism, we first need to understand the dimensions of the prism.

Given dimensions:

  • Height: 10 ft
  • Width: 6 ft
  • Length: 3 ft

When a horizontal plane intersects the prism, the resulting cross section will be shaped based on the dimensions of the top face of the prism. Since we're cutting through horizontally, the cross section will be parallel to the base of the prism.

Since the base of the prism is rectangular with dimensions 3 ft by 6 ft, a horizontal cross-section of the prism will also be a rectangle with the same length (3 ft) and width (6 ft) as the base of the prism.

Part 1:

Based on the dimensions and the description of the resulting cross section, the correct answer is:

B. The cross section is a rectangle which has the same length and width as the prism.

Regarding your second question about the possibility of having a horizontal cross section with different dimensions if you intersect the prism in another spot: the dimensions of the cross section will remain the same as long as the horizontal cut is made through the prism at any height. The cross section will always be 3 ft by 6 ft for any horizontal cut. Hence, the cross section cannot have different dimensions; it will always reflect the base dimensions of the prism.