Answer :
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.
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.
