Answered

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Given the conversion factor [tex]\(\frac{12 \text{ in}}{1 \text{ ft}}\)[/tex], which has the larger volume?

A. Cube A
B. Cube B
C. They are the same size.

Sagot :

GinnyAnswer
To determine which cube has the larger volume, we'll start by understanding the dimensions and converting the measurements to a common unit.

We are given:
- Side of Cube A: 1 foot
- Side of Cube B: 12 inches

Since 1 foot is equal to 12 inches, we convert the side of Cube A from feet to inches:
[tex]\[ 1 \text{ ft} = 12 \text{ in} \][/tex]

Now, let's calculate the volumes of the cubes in cubic inches.

1. Volume of Cube A:
[tex]\[ \text{Volume}_A = (\text{side}_A)^3 = (12 \text{ in})^3 \][/tex]
[tex]\[ \text{Volume}_A = 12^3 = 1728 \text{ cubic inches} \][/tex]

2. Volume of Cube B:
[tex]\[ \text{Volume}_B = (\text{side}_B)^3 = (12 \text{ in})^3 \][/tex]
[tex]\[ \text{Volume}_B = 12^3 = 1728 \text{ cubic inches} \][/tex]

After calculating the volumes:
- Volume of Cube A: 1728 cubic inches
- Volume of Cube B: 1728 cubic inches

By comparing the volumes, you can see that:
[tex]\[ \text{Volume}_A = \text{Volume}_B \][/tex]

Thus, the correct answer is:
C. They are the same size.
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