To solve the problem of finding the surface area (SA) and volume (V) of each cube, we need to use the following formulas:
1.
Surface Area (SA) of a Cube:
\[
SA = 6s^2
\]
where \( s \) is the length of one side of the cube.
2.
Volume (V) of a Cube:
\[
V = s^3
\]
where \( s \) is the length of one side of the cube.
Let's go through each cube step by step:
Cube 1: Side length \( s = 1 \)
-
Surface Area:
\[
SA = 6 \times 1^2 = 6 \times 1 = 6
\]
-
Volume:
\[
V = 1^3 = 1
\]
Cube 2: Side length \( s = 2 \)
-
Surface Area:
\[
SA = 6 \times 2^2 = 6 \times 4 = 24
\]
-
Volume:
\[
V = 2^3 = 8
\]
Cube 3: Side length \( s = 3 \)
-
Surface Area:
\[
SA = 6 \times 3^2 = 6 \times 9 = 54
\]
-
Volume:
\[
V = 3^3 = 27
\]
Cube 4: Side length \( s = 4 \)
-
Surface Area:
\[
SA = 6 \times 4^2 = 6 \times 16 = 96
\]
-
Volume:
\[
V = 4^3 = 64
\]
Cube 5: Side length \( s = 5 \)
-
Surface Area:
\[
SA = 6 \times 5^2 = 6 \times 25 = 150
\]
-
Volume:
\[
V = 5^3 = 125
\]
Cube 6: Side length \( s = 6 \)
-
Surface Area:
\[
SA = 6 \times 6^2 = 6 \times 36 = 216
\]
-
Volume:
\[
V = 6^3 = 216
\]
Cube 7: Side length \( s = 7 \)
-
Surface Area:
\[
SA = 6 \times 7^2 = 6 \times 49 = 294
\]
-
Volume:
\[
V = 7^3 = 343
\]
Cube 8: Side length \( s = 8 \)
-
Surface Area:
\[
SA = 6 \times 8^2 = 6 \times 64 = 384
\]
-
Volume:
\[
V = 8^3 = 512
\]
Cube 9: Side length \( s = 9 \)
-
Surface Area:
\[
SA = 6 \times 9^2 = 6 \times 81 = 486
\]
-
Volume:
\[
V = 9^3 = 729
\]
Cube 10: Side length \( s = 10 \)
-
Surface Area:
\[
SA = 6 \times 10^2 = 6 \times 100 = 600
\]
-
Volume:
\[
V = 10^3 = 1000
\]
Cube 11: Side length \( s = 11 \)
-
Surface Area:
\[
SA = 6 \times 11^2 = 6 \times 121 = 726
\]
-
Volume:
\[
V = 11^3 = 1331
\]
Cube 12: Side length \( s = 12 \)
-
Surface Area:
\[
SA = 6 \times 12^2 = 6 \times 144 = 864
\]
-
Volume:
\[
V = 12^3 = 1728
\]
Final Answers:
\[
\boxed{
\begin{array}{c|c|c}
\text{Cube} & \text{Surface Area (SA)} & \text{Volume (V)} \\
\hline
1 & 6 & 1 \\
2 & 24 & 8 \\
3 & 54 & 27 \\
4 & 96 & 64 \\
5 & 150 & 125 \\
6 & 216 & 216 \\
7 & 294 & 343 \\
8 & 384 & 512 \\
9 & 486 & 729 \\
10 & 600 & 1000 \\
11 & 726 & 1331 \\
12 & 864 & 1728 \\
\end{array}
}
\]
Parent Tip: Review the logic above to help your child master the concept of finding area and volume worksheet.
