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Volumes Practice Test 1

Question : 2 of 40

Marks: +1, -0

Solution: 👈: Video Solution

Concept:

When cubes are melted and recast, the total volume remains unchanged.

Explanation:

Volume of first cube

= 6^3 = 216\ \mathrm{cm}^3

Volume of second cube

= 8^3 = 512\ \mathrm{cm}^3

Volume of third cube

= 10^3 = 1000\ \mathrm{cm}^3

Total volume

= 216 + 512 + 1000 = 1728\ \mathrm{cm}^3

Let the edge of the new cube be

a

Then

a^3 = 1728

So,

a = \sqrt[3]{1728} = 12\ \mathrm{cm}

Diagonal of a cube

= a\sqrt{3}

Thus, diagonal

= 12\sqrt{3}

Using

\sqrt{3} \approx 1.73

, diagonal

= 12 \times 1.73 = 20.76 \approx 20.8\ \mathrm{cm}

Answer:

The diagonal of the new cube is

20.8\ \mathrm{cm}

, so option B is correct.

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