Question

1. this net folds into the cube shown beside it. on the cube, which letter will be on the side opposite d?

options: b, e, a, c

Explanation:

Step1: Analyze the cube net structure

In a cube net, opposite faces are not adjacent. The net here has a central square \( C \), with \( B \) adjacent to \( C \), \( D \) adjacent to \( C \), \( A \) adjacent to \( B \), \( F \) above \( C \), \( E \) below \( C \).

Step2: Determine opposite of D

Looking at the net, the face adjacent to \( D \) are \( C \), \( E \), \( F \)? Wait, no. Let's list adjacents: For \( D \), adjacent faces are \( C \), and the ones next to \( C \) in the row. Wait, the net is a cross: \( A - B - C - D \) in a row, with \( F \) above \( C \) and \( E \) below \( C \). So when folded, \( A \) is opposite \( C \)? No, wait, in a cross - shaped net (the "plus" sign net), the opposite of \( B \) is \( D \)? No, wait, let's think again. In the net, the faces: \( A \) is adjacent to \( B \), \( B \) is adjacent to \( A \) and \( C \), \( C \) is adjacent to \( B \), \( D \), \( F \), \( E \), \( D \) is adjacent to \( C \), so the opposite of \( D \) should be \( B \)? Wait no, wait the options are \( B \), \( E \), \( A \), \( C \). Wait, no, let's correct. In the net, the row is \( A \), \( B \), \( C \), \( D \). So when folded into a cube, \( A \) is opposite \( C \)? No, no. Wait, in a cube net where you have a central square ( \( C \) ) with four squares around it ( \( A \), \( B \), \( D \), and one more? Wait, the net is: top \( F \), middle row \( A \), \( B \), \( C \), \( D \), bottom \( E \). So when folded, \( F \) is opposite \( E \), \( A \) is opposite \( C \)? No, no, that's wrong. Wait, no: in a cube, each face has one opposite. Let's take the net: the faces adjacent to \( C \) are \( B \), \( D \), \( F \), \( E \). So the only face not adjacent to \( C \) is \( A \)? No, that can't be. Wait, no, the middle row: \( A \) is next to \( B \), \( B \) next to \( A \) and \( C \), \( C \) next to \( B \), \( D \), \( F \), \( E \), \( D \) next to \( C \). So the opposite of \( D \): let's see, when you fold the net, \( B \) and \( D \) are on opposite sides? Wait, no, let's use the standard cube net rules. In a "cross" net (with a central square and four around it, plus top and bottom), the opposite of the square to the left of center ( \( B \) ) is the square to the right of center ( \( D \) )? No, that's not right. Wait, no, actually, in this net, the faces: \( A \) is opposite \( C \)? No, I think I made a mistake. Wait, let's list all pairs:

- \( F \) is opposite \( E \) (top and bottom)
- \( A \) is opposite \( C \)? No, no, \( A \) is adjacent to \( B \), \( B \) adjacent to \( A \) and \( C \), \( C \) adjacent to \( B \), \( D \), \( F \), \( E \), so \( A \) is adjacent to \( B \), so \( A \)'s opposite can't be \( B \). Wait, maybe \( B \) is opposite \( D \), and \( A \) is opposite \( C \), \( F \) opposite \( E \). Let's check: if we fold the net, \( A \) and \( C \) are on opposite sides? No, when you fold \( A \) towards \( B \), \( B \) towards \( C \), \( D \) towards \( C \), so \( A \) and \( D \) are not opposite. Wait, maybe the correct opposite of \( D \) is \( B \)? No, the options include \( B \) as an option. Wait, let's re - examine the net:

The net is:

Top: \( F \)

Middle: \( A \) \( B \) \( C \) \( D \)

Bottom: \( E \)

When folding into a cube, the face \( B \) is adjacent to \( A \), \( C \), \( F \), \( E \)? No, when folding, \( B \) will be adjacent to \( A \) (left), \( C \) (right), \( F \) (top), \( E \) (bottom). Then \( D \) is adjacent to \( C \) (left), \( F \) (top), \( E \) (bottom), and the face opposite to \( D \) would be \( B \), because \( B \) and \( D \) are on opposite sides of the central \( C \) in the middle row. Wait, no, in the middle row, \( A - B - C - D \), so \( A \) is opposite \( C \), \( B \) is opposite \( D \), \( F \) opposite \( E \). Yes, that makes sense. So the letter opposite \( D \) is \( B \).

Answer:

B