question_answer 1)

                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) \[a,\,2b,\,3c\].

Answer:

                (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 \[=(a)\times (2b)\times (3c)\] \[=(2\times 3)\times (a\times b\times c)\] \[=6abc\].