Three cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find…
2019
Three cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find half of the surface area of the new cube.
Answer: D. 243 cm² — Concept When solid cubes are melted and recast without material loss, total volume is conserved. For a cube of side a, volume is a3 and total surface area is…
- A.
293 cm²
- B.
463 cm²
- C.
486 cm²
- D.
243 cm²
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Show answer & explanation
Correct answer: D
Concept
When solid cubes are melted and recast without material loss, total volume is conserved.
For a cube of side a, volume is a3 and total surface area is 6a2; therefore half of its surface area is 3a2.
Application
Add the original volumes: 13 + 63 + 83 = 1 + 216 + 512 = 729 cm3.
Let the side of the new cube be x cm. Volume conservation gives x3 = 729.
Taking the cube root gives x = 9 cm.
Half of the surface area of the new cube is 3x2 = 3 × 92 = 3 × 81 = 243 cm2.
Cross-check
The full surface area is 6 × 92 = 486 cm2, and half of 486 cm2 is 243 cm2. Hence the required value is 243 cm2.