Question:
Three cubes of metal with edges 3 cm, 4 cm, and 5 cm respectively are melted to form a single cube. What is the lateral surface area of the new formed cube?
Three cubes of metal with edges 3 cm, 4 cm, and 5 cm respectively are melted to form a single cube. What is the lateral surface area of the new formed cube?
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When combining cubes, sum their volumes, then find the new side and compute the area.
Updated On: Oct 27, 2025
- \( 72 \) cm\(^2\)
- \( 144 \) cm\(^2\)
- \( 128 \) cm\(^2\)
- \( 256 \) cm\(^2\)
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The Correct Option is B
Solution and Explanation
Total volume of the three cubes:
\[ V = 3^3 + 4^3 + 5^3 = 27 + 64 + 125 = 216 \] New cube's side:
\[ s = \sqrt[3]{216} = 6 \text{ cm} \] Lateral surface area of the new cube:
\[ \text{LSA} = 4s^2 = 4(6)^2 = 144 \text{ cm}^2 \]
\[ V = 3^3 + 4^3 + 5^3 = 27 + 64 + 125 = 216 \] New cube's side:
\[ s = \sqrt[3]{216} = 6 \text{ cm} \] Lateral surface area of the new cube:
\[ \text{LSA} = 4s^2 = 4(6)^2 = 144 \text{ cm}^2 \]
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