A big rubik's cube is made whose dimension is $20 \times 20 \times 20$ . Find the diffrence in volume of the bigger one and a smaller one whose dimension is $19 \times 19 \times 19$ . [2 MARKS]

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Solution

Concept: 1 Mark
Application: 1 Mark

Difference in volume
$= 20^{3} - 19^{3}$

$[x^{3} - y^{3} = (x - y)^{3} + 3 x y (x - y)]$

$= (20 - 19)^{3} + 3 \times 20 \times 19 (20 - 19)$

$= 1 + 3 \times 20 \times 19 (1)$

$= 1141$

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