Let’s solve each problem one by one. We’ll calculate surface area for cubes and rectangular prisms step by step.
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Problem 1: Vanessa’s cube
She has a
cube with side length = 4 inches.
A cube has
6 identical square faces.
Area of one face = side × side = 4 × 4 =
16 square inches
Total surface area = 6 × 16 =
96 square inches
✔ So, Vanessa needs to cover
96 in² with photos.
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Problem 2: Mila’s toy bin (rectangular prism)
Dimensions:
Length = 2 feet
Width = 1 foot
Height = 2 feet
Surface area of a rectangular prism =
2×(length×width + length×height + width×height)
Plug in the numbers:
= 2×(2×1 + 2×2 + 1×2)
= 2×(2 + 4 + 2)
= 2×8 =
16 square feet
✔ Mila stained
16 ft²
*(Note: The lid is included — since it says “including the top of the lid and the bottom”, we’re calculating full surface area, which already includes all 6 sides.)*
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Problem 3: Emmanuel’s die (cube)
Side length = 1.6 centimeters
One face area = 1.6 × 1.6 =
2.56 cm²
He paints
one die, which has 6 faces → but wait! He wants to paint
one of the dice blue — meaning he’s painting the entire outer surface of one cube-shaped die.
So total area = 6 × 2.56 = let’s compute:
2.56 × 6 =
2 × 6 = 12
0.56 × 6 = 3.36
Total = 12 + 3.36 =
15.36 cm²
✔ Emmanuel will paint
15.36 cm²
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Problem 4: Terrell’s tissue box (rectangular prism)
Dimensions:
Length = 11 inches
Width = 6 inches
Height = 5 inches
Surface area = 2×(lw + lh + wh)
= 2×(11×6 + 11×5 + 6×5)
= 2×(66 + 55 + 30)
= 2×(151) =
302 square inches
✔ Terrell needs
302 in² of construction paper.
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Final Answer:
1. 96 square inches
2. 16 square feet
3. 15.36 square centimeters
4. 302 square inches
Parent Tip: Review the logic above to help your child master the concept of surface area problems worksheet.
