Multiple choice

Three solid cubes of metal have sides 6 cm, 8 cm and 10 cm, respectively. They are melted to form a new cube. What is the surface area of this new cube?

  1. 915 cm2

  2. 864 cm2

  3. 950 cm2

  4. 812 cm2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The volume of the new cube is the sum of the volumes of the three smaller cubes: 6^3 + 8^3 + 10^3 = 216 + 512 + 1000 = 1728 cm^3. The side length of the new cube is the cube root of 1728, which is 12 cm. The surface area is 6 * (side^2) = 6 * 144 = 864 cm^2.

AI explanation

The new cube is formed by melting the three cubes, so its volume equals the sum of their individual volumes, calculated as 6 cubed plus 8 cubed plus 10 cubed. This gives 216 plus 512 plus 1000, totaling 1728 cubic cm, meaning the side of the new cube is the cube root of 1728 which is 12 cm. The surface area of a cube is 6 times the side squared, so we calculate 6 times 12 squared to get 864 square cm.

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