Question

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) $xy,2x^{2}y,2x{y}^2$

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

Answer 1

We know that,

Volume of rectangular box (Cuboidal in shape) $=$ Length$\times$Breadth$\times$Height

(i) Length, breadth and height of rectangular box are $5a,3a^2,7a^4$

Volume of the rectangular box for given dimensions $=5a\times 3a^2\times 7a^4=5\times 3\times 7\times a\times a^2\times a^4=105a^7$ [$\because a^m\times b^n=a^{m+n}$]

(ii) Length, breadth and height of rectangular box are $2p,4q,8r$

Volume of the rectangular box for given dimensions $=2p\times 4q\times 8r=2\times 4\times 8\times p\times q\times r=64pqr$

(iii) Length, breadth and height of rectangular box are $xy,2x^{2}y,2x{y}^2$

Volume of the rectangular box for given dimensions

$=xy\times 2x^{2}y\times 2x{y}^2=2\times 2\times xy\times x^{2}y\times x{y}^2=4x^4{y}^4$

(iv) Length, breadth and height of rectangular box are $a,2b,3c$

Volume of the rectangular box for given dimensions

$=a\times 2b\times 3c=2\times 3\times a\times b\times c=6abc$