Question:
A wooden cuboidal box with lid has external dimensions 80 cm × 49 cm × 30 cm. If thickness of the wood is 2 cm, then find the volume of the wood (in cm³) used.
A wooden cuboidal box with lid has external dimensions 80 cm × 49 cm × 30 cm. If thickness of the wood is 2 cm, then find the volume of the wood (in cm³) used.
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For box with lid, subtract 2×thickness from each dimension
Updated On: Apr 21, 2026
- 28420
- 28620
- 28680
- 29940
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The Correct Option is C
Solution and Explanation
Step 1: External dimensions of the cuboidal box are \(80 \times 49 \times 30\).
External volume \(= 80 \times 49 \times 30 = 117600\ \text{cm}^3\)
Step 2: Thickness of wood = 2 cm on each side. So, each dimension reduces by \(2 + 2 = 4\) cm for internal cavity.
Step 3: Internal dimensions: Length \(= 80 - 4 = 76\), Breadth \(= 49 - 4 = 45\), Height \(= 30 - 4 = 26\)
Step 4: Internal volume \(= 76 \times 45 \times 26\) \(= (76 \times 45) \times 26 = 3420 \times 26 = 88920\ \text{cm}^3\)
Step 5: Volume of wood used \(=\) External volume \(-\) Internal volume \(= 117600 - 88920 = 28680\ \text{cm}^3\)
Step 2: Thickness of wood = 2 cm on each side. So, each dimension reduces by \(2 + 2 = 4\) cm for internal cavity.
Step 3: Internal dimensions: Length \(= 80 - 4 = 76\), Breadth \(= 49 - 4 = 45\), Height \(= 30 - 4 = 26\)
Step 4: Internal volume \(= 76 \times 45 \times 26\) \(= (76 \times 45) \times 26 = 3420 \times 26 = 88920\ \text{cm}^3\)
Step 5: Volume of wood used \(=\) External volume \(-\) Internal volume \(= 117600 - 88920 = 28680\ \text{cm}^3\)
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