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4.Obtain the volume of rectangular boxes with the following length, breadth and height respectively.
(i) \(5a, 3a^2, 7a^4\)

(ii) \(2p, 4q, 8r\)

(iii) \(xy, 2x^2y, 2xy^2\)

(iv) \(a, 2b, 3c\)

Answer :

(i)Given that, length = 5a, breadth = \(3a^2\), height = \(7a^4\)

∴Volume of the box =\( l \times b \times h = 5a \times 3a^2 \times 7a^4 = 105 a^7 \;\)cu. units

(ii)Given that, length = 2p, breadth = 4q, height = 8r

∴Volume of the box =\( l \times b \times h = 2p \times 4q \times 8r = 64pqr\;\) cu. units

(iii)Given that, length = xy, breadth =\( 2x^2y\), height = 2xy^2\)

Volume of the box =\( l \times b \times h = xy \times 2x^2y \times 2xy^2 = (1 \times 2 \times 2) \times xy \times x^2y \times xy^2 = 4x^4y^4 \;\)cu. units

(iv)Given that, length = a, breadth = 2b, height = 3c

∴Volume of the box = \(l \times b \times h = a \times 2b \times 3c = (1 \times 2 \times 3)abc = 6 abc\;\) cu. units