To find the difference in volume between a 13 ft. cube and a 10 ft. cube, we need to follow these steps:
1. Calculate the volume of the 13 ft. cube.
2. Calculate the volume of the 10 ft. cube.
3. Subtract the volume of the 10 ft. cube from the volume of the 13 ft. cube to get the difference in volume.
First, let's recall that the volume [tex]\( V \)[/tex] of a cube with side length [tex]\( s \)[/tex] is given by:
[tex]\[ V = s^3 \][/tex]
### Step-by-Step Solution
1. Calculate the volume of the 13 ft. cube:
[tex]\[
\text{Volume of 13 ft. cube} = 13^3 = 13 \times 13 \times 13
\][/tex]
[tex]\[
= 169 \times 13
\][/tex]
[tex]\[
= 1690 + 507
\][/tex]
[tex]\[
= 2197 \text{ cubic ft.}
\][/tex]
2. Calculate the volume of the 10 ft. cube:
[tex]\[
\text{Volume of 10 ft. cube} = 10^3 = 10 \times 10 \times 10
\][/tex]
[tex]\[
= 1000 \text{ cubic ft.}
\][/tex]
3. Find the difference in volume:
[tex]\[
\text{Difference in volume} = 2197 \text{ cubic ft.} - 1000 \text{ cubic ft.}
\][/tex]
[tex]\[
= 1197 \text{ cubic ft.}
\][/tex]
Therefore, the difference in volume between a 13 ft. cube and a 10 ft. cube is [tex]\( \boxed{1197 \text{ cubic ft.}} \)[/tex].
So, the correct answer is:
[tex]\[
\text{B. 1197 cubic ft.}
\][/tex]
