Question

7 8.8.8 quiz: cross sections of three - dimensional solids
javin cuts a block of wood along the red line. when he looks at the newly

• exposed face, what is the shape of the cross - section?

a. a rectangle, 4 inches by 2 inches
b. a square, 2 inches by 2 inches
c. a rectangle, 4 inches by 3 inches
d. a rectangle, 2 inches by 3 inches

Explanation:

Step1: Analyze the cross - section

When a rectangular prism (the block of wood) is cut parallel to its length and width (as indicated by the red line in the problem, assuming the standard orientation of the prism with given length \(l = 4\) in, height \(h=3\) in, and if we assume the cut is made such that the height of the cross - section related to the height of the prism is not fully used. If we assume the cut is made at a height of \(2\) in (since the height of the prism is \(3\) in, and if we consider the dimension along the length of the prism is \(4\) in. The cross - section of a rectangular prism, when cut parallel to two of its adjacent faces (length and height in this case, assuming the cut is made at a certain height level), has the shape of a rectangle. The length of the rectangle is the same as the length of the prism (\(l = 4\) in), and the width of the rectangle is the height of the cut section. If we assume the cut is made such that the non - height dimension related to the cross - section is \(2\) in (maybe from the total height of \(3\) in, if we consider the cross - section's two dimensions: one is the length of the prism \(4\) in and the other is \(2\) in (assuming the cut is made parallel to the base and top faces at a height that gives a \(2\) in dimension).

Answer:

A. A rectangle, 4 inches by 2 inches