question_answer 1)

                There are two cuboidal boxes as shown in the adjoining figure. Which box requires the lesser amount of material to make? (a)                       (b)

Answer:

                First Cuboidal Box \[l=60\,cm\] \[b=40\,cm\] \[h=50\,cm\] \[\therefore \] Total surface area \[=2(lb+bh+hl)\] \[=2(60\times 40+40\times 50+50\times 60)\,c{{m}^{2}}\] \[=2(2400\,+2000+3000)\,c{{m}^{2}}\] \[=2(7400)\,c{{m}^{2}}\] \[=14800\,c{{m}^{2}}\] Second Cuboidal Box \[l=50\,cm\] \[b=50\,cm\] \[h=50\,cm\] \[\therefore \] Total surface area \[=2(lb+bh+hl)\] \[=2(50\times 50+50\times 50+50\times 50)\,c{{m}^{2}}\] \[=2(2500+2500+2500)\,c{{m}^{2}}\] \[=2(7500)\,c{{m}^{2}}\] \[=15000\,\,c{{m}^{2}}\] Hence, the box (a) requires the least amount of material to make.