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.
- A.
293 cm²
- B.
463 cm²
- C.
486 cm²
- D.
243 cm²
Attempted by 43 students.
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Correct answer: D
Solution:
Compute volumes of the three cubes and add them to get the volume of the new cube.
Volume of cube with side 1 cm = 1^3 = 1 cm³.
Volume of cube with side 6 cm = 6^3 = 216 cm³.
Volume of cube with side 8 cm = 8^3 = 512 cm³.
Total volume = 1 + 216 + 512 = 729 cm³.
Find the side length of the new cube: cube root of total volume.
Side length = cube root(729) = 9 cm.
Surface area of a cube = 6 × side^2.
Surface area = 6 × 9^2 = 6 × 81 = 486 cm².
Half of the surface area = 486 ÷ 2 = 243 cm²