Question

Rosa cut 2 equal-sized cakes as shown in the picture.

Benjamin said, "I will take a piece from either cake, because all the pieces are the same amount of cake."

Use the drop-down menus to complete statements about Benjamin's thinking.

Cake A: A circle split in half by a horizontal line. Cake B: A circle split in half by a vertical line.
CLEAR CHECK
Benjamin is
.

The pieces in Cake A are
the pieces in Cake B.

The cakes are cut in different ways,
.

Answer 1

Explanation:

Benjamin is correct in thinking that all the pieces are the same amount of cake.

In Cake A, the pieces are two semicircles formed by splitting the circle horizontally.

In Cake B, the pieces are two semicircles formed by splitting the circle vertically.

Although the cakes are cut in different ways, the resulting pieces are the same size because the area of each piece depends on the proportion of the total area of the cake it represents. Since both cakes are divided into two equal parts, each piece will have half of the total cake's area, making them the same amount of cake.

Answer 2

Based on the description of the cakes, Cake A is a circle split in half by a horizontal line, and Cake B is a circle split in half by a vertical line. Since both cakes are equal-sized and each is divided into two equal parts, Benjamin's thinking is correct.

Here are the statements about Benjamin's thinking:

1. Benjamin is correct.

2. The pieces in Cake A are equal to the pieces in Cake B.

3. The cakes are cut in different ways, but the pieces are still equal in size.