Question

The volume of cube is 512cm³. What will be the volume of another cube whose sides are double the side of this cube ?

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Answer 1

Step-by-step explanation:

$volume \: of \: cube = 512 {cm}^{3} \\ {side}^{3} = 512 {cm}^{3} \\ side = \sqrt[3]{512} \\ side = 8cm \\ then \: side \: of \: another \: cube = 2 \times 8 \\ = 16cm \\ volume \: of \: another \: cube = {side}^{3} \\ = {16}^{3} \\ = 16 \times 16 \times 16 \\ = 4096 {cm}^{3}$

Answer 2

Step-by-step explanation:

The first cube has a volume of 512 cm^3. Say a^3 = 512 cm^3. So the new cube has its edges double that of the first cube, hence it volume should be (2a)^3 or 2^3*a^3 = 8*a^3 that is it will be 8 times the earlier volume or 8*512 = 4096 cm^3.

Let’s see whether it is actually so.

We notice a^3 = 512 cm^3 = 8^3 cm^3. Therefore a = 512^(1/3) =8 cm.

The new cube has its edges as 2a or 16 cm. So new volume = 16^3 = 4096 cm^3, same as seen earlier. Hence proved.