Let’s solve each problem one by one. Remember: a cube has 6 identical square faces. So, if you know the width (side length) of one face, you can find the surface area by:
Surface Area = 6 × (width × width)
Or if you’re given the surface area and need to find the width:
Width = √(Surface Area ÷ 6)
We’ll go through each question carefully.
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1) Width = 7 cm → Find Surface Area
Each face is 7 cm × 7 cm = 49 cm²
There are 6 faces → 6 × 49 =
294 cm²
✔ Check: 7×7=49; 49×6=294 → Correct.
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2) Surface Area = 24 in² → Find Width
Divide total surface area by 6: 24 ÷ 6 = 4
Now take square root: √4 =
2 inches
✔ Check: 2×2=4; 4×6=24 → Correct.
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3) Width = 11 cm → Find Surface Area
Each face: 11 × 11 = 121 cm²
Total: 6 × 121 =
726 cm²
✔ Check: 11×11=121; 121×6=726 → Correct.
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4) Surface Area = 600 ft² → Find Width
600 ÷ 6 = 100
√100 =
10 feet
✔ Check: 10×10=100; 100×6=600 → Correct.
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5) Width = 3½ m → Find Surface Area
First, write 3½ as a fraction: 7/2
Area of one face: (7/2) × (7/2) = 49/4
Multiply by 6: 6 × 49/4 = (6/1) × (49/4) = 294/4 = 73.5 m²
✔ Or decimal: 3.5 × 3.5 = 12.25; 12.25 × 6 = 73.5 → Correct.
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6) Surface Area = 150 in² → Find Width
150 ÷ 6 = 25
√25 =
5 inches
✔ Check: 5×5=25; 25×6=150 → Correct.
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7) Width = 30 cm → Find Surface Area
30 × 30 = 900 cm² per face
6 × 900 =
5400 cm²
✔ Check: 30×30=900; 900×6=5400 → Correct.
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8) Surface Area = 216 in² → Find Width
216 ÷ 6 = 36
√36 =
6 inches
✔ Check: 6×6=36; 36×6=216 → Correct.
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Final Answer:
1) 294
2) 2
3) 726
4) 10
5) 73.5
6) 5
7) 5400
8) 6
Parent Tip: Review the logic above to help your child master the concept of surface area of cube worksheet.
