Obtain the volume of rectangular boxes with following length, breadth and height given respectively.
(i) $5 a, 3 a^{2}, 7 a^{4}$
(ii) $2 p, 4 q, 8 r$
(iii) $x y, 2 x^{2} y, 2 x y^{2}$
(iv) $a, 2 b, 3 c$

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Solution

Volume $= Length \times Breadth \times Height$
$V = l \times b \times h$
(i) $V = 5 a \times 3 a^{2} \times 7 a^{4} = 105 a^{(1 + 2 + 4)} = 105 a^{7}$

(ii) $V = 2 p \times 4 q \times 8 r = 64 p q r$

(iii) $V = x y \times 2 x^{2} y \times 2 x y^{2}$ $= 4 x^{(1 + 2 + 1)} y^{(1 + 1 + 2)} = 4 x^{4} y^{4}$

(iv) $V = a \times 2 b \times 3 c = 6 a b c$

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