Word Problem 2

Problem 2: If there are three metallic cubes with sides of 3 cm, 4 cm and5 cm respectively, and if these cubes are melted together to make one cube, what will be the side of the new cube?


There are three metallic cube boxes and suppose there volumes are V1, V2, and V3

Now let us calculate volumes of each cube box;

We use formula for calculation of volume;

Volume = Side1 \times Side2 \times Side3

For cube Box with each side of 3cm;

Volume1 = 3 \times 3 \times 3 = 27 cm^{3}For cube Box with each side of 4cm;

Volume2 = 4 \times 4 \times 4 = 64 cm^{3}

For cube Box with each side of 5cm;

Volume2 = 5 \times 5 \times 5 = 125 cm^{3}

Now suppose when all these three  boxes are melted and mixed to form a single box, the each side of that single cube box is ‘y’

So, then for that single cube box ;

Volume = V = y \times y \times y = y cm^{3}

But this volume of single cube box should be equal to sum of volumes of all three above cube boxes !


V = Volume1 + Volume2+ Volume3

 \Rightarrow y^{3}= 27+64+125

 \Rightarrow y^{3}= 216

 \Rightarrow y^{3}= 8^{3}

Cancel out powers on both sides;

 \Rightarrow y}= 8

So, each side of coalesced  cube is 8 cm length

So, Volume of new coalesced cube ;

Volume=V= 8\times 8\times 8 =512 cm^{3}

(basic mathematics for general public)




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