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Question

If the edge of a cube is increased by 2cm, the volume will increase by 488cm2. What then will be the new length of each edge of the cube

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Solution

Let the length of the edge of the cube be x

Length after 2cm increase =x+2

Then original Volume of the cube = (Length)3

That is, Volume =x3

New Volume =(x+2)3

Given that after increasing the length of the edge, the volume is increased by 488cm2

(x+2)3x3=488

x3+6x2+12x+8x3=488

6x2+12x480=0

x2+2x80=0

(x8)(x+10)=0

x=8orx=10(x10,xcannotbenegative)

Therefore the length of each edge of the cube is 8+2=10cm


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