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

(i)$5a,\,3{{a}^{2}},\,7{{a}^{4}}$                 Volume of the rectangular box                 = Length $\times$ Breadth $\times$ Height                 $=(5a)\times (3{{a}^{2}})\times (7{{a}^{4}})$                 $=(5\times 3\times 7)\times (a\times {{a}^{2}}\times {{a}^{4}})$                 $=105\,{{a}^{7}}$ (ii) $2p,\,4q,\,8r$ Volume of the rectangular box = Length $\times$ Breadth $\times$ Height $=(2p)\times (4q)\times (8r)$ $=(2\times 4\times 8)\times (p\times q\times r)$ $=64\,pqr$ (iii) $xy,\,2{{x}^{2}}y,\,2x{{y}^{2}}$ Volume of the rectangular box = Length $\times$ Breadth $\times$ Height $=(xy)\times (2{{x}^{2}}y)\times (2x{{y}^{2}})$ $=(2\times 2)\times (x\times {{x}^{2}}\times x)\times (y\times y\times {{y}^{2}})$ $=4{{x}^{4}}{{y}^{4}}$ (iv) $a,\,2b,\,3c$ Volume of the rectangular box = Length $\times$ Breadth $\times$ Height $=(a)\times (2b)\times (3c)$ $=(2\times 3)\times (a\times b\times c)$ $=6abc$.