Explanation:
We are asked to find either the
surface area (SA) or the
volume (V) of each cube.
A cube has all sides equal, so if the side length is $ s $:
-
Surface Area of a cube = $ 6 \times s^2 $
(because a cube has 6 faces, each face is a square with area $ s^2 $)
-
Volume of a cube = $ s^3 $
(length × width × height = $ s \times s \times s $)
Now go one by one:
1.
1·SA: side = 12″
SA = $ 6 \times 12^2 = 6 \times 144 = 864 $ in²
2.
2·V: side = 8″
V = $ 8^3 = 8 \times 8 \times 8 = 512 $ in³
3.
3·SA: side = 24″
SA = $ 6 \times 24^2 = 6 \times 576 = 3456 $ in²
4.
4·V: side = 25″
V = $ 25^3 = 25 \times 25 \times 25 = 625 \times 25 = 15,625 $ in³
5.
5·SA: side = 70″
SA = $ 6 \times 70^2 = 6 \times 4900 = 29,400 $ in²
6.
6·SA: side = 5″
SA = $ 6 \times 5^2 = 6 \times 25 = 150 $ in²
7.
7·V: side = 4″
V = $ 4^3 = 64 $ in³
8.
8·V: side = 6″
V = $ 6^3 = 216 $ in³
9.
9·SA: side = 13″
SA = $ 6 \times 13^2 = 6 \times 169 = 1014 $ in²
10.
10·V: side = 3″
V = $ 3^3 = 27 $ in³
Let me double-check each calculation quickly:
- 12² = 144 → ×6 = 864
✔
- 8³ = 512
✔
- 24² = 576 → ×6 = 3456
✔
- 25² = 625 → ×25 = 15,625
✔
- 70² = 4900 → ×6 = 29,400
✔
- 5² = 25 → ×6 = 150
✔
- 4³ = 64
✔
- 6³ = 216
✔
- 13² = 169 → ×6 = 1014
✔
- 3³ = 27
✔
All correct.
Final Answer:
1. 864 in²
2. 512 in³
3. 3456 in²
4. 15625 in³
5. 29400 in²
6. 150 in²
7. 64 in³
8. 216 in³
9. 1014 in²
10. 27 in³
Parent Tip: Review the logic above to help your child master the concept of surface area of cube worksheet.
