Question

2. A metal cube is melted to form four new smaller cubes of equal volume. What is the ratio of the total
surface area of the original cube to that of one of the smaller cubes​

Answer 1

Answer:

answer : \sqrt[3]{16}

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16

explanation : a metal cube is melted to form four new smaller cubes of equal volume.

so, volume of original cube = 4 × volume of smaller cube

Let side length of original cube is L and smaller cube is l.

so, L³ = 4l³ => L = \sqrt[3]{4}

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4

l....(1)

now, surface area of original cube , A = 6L²

from equation (1),

A = 6\sqrt[3]{16}

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l²

and surface area of one of the smaller cubes , a = 6l²

now ratio of the total surface area of the original cube to that of one of the smaller cubes = A/a = 6\sqrt[3]{16}

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16

l² /6l² = \sqrt[3]{16}

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16