question_answer 1)

                Daniel is painting the walls and ceiling of a cuboidal Hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint \[100\,\,{{m}^{2}}\] of area is painted.                                 How many cans of paint will she need to paint the room?                       

Answer:

                \[l=15\,m\]                 \[b=10\,m\]                 \[h=7\,m\] Surface area to be painted \[=2(l\times b+b\times h+h\times l)-l\times b\] \[=2(15\times 10+10\times 7+7\times 15)\,{{m}^{2}}\] \[-(15\times 10){{m}^{2}}\]                 \[=2(150+70+105)\,{{m}^{2}}-150\,{{m}^{2}}\] \[=2(325)\,{{m}^{2}}-150\,{{m}^{2}}\] \[=650\,{{m}^{2}}-150\,{{m}^{2}}\] \[=500\,{{m}^{2}}\] \[\therefore \] Number of cans needed \[=\frac{\text{Surface}\,\text{area}\,\text{to}\,\text{the}\,\text{painted}}{\text{Area}\,\text{painted}\,\text{by}\,\text{1}\,\text{can}}\] \[=\frac{500}{100}\] = 5 Hence, she will need 5 cans of paint to paint the room.