a box with lid is made by the piece of wood 2.5 cm thick its outside length breadth and height are 80cm 60 cm and 50 cm. then find the volume of wood required to make the box and find the cost of painting the outside of the box at the rate of rs 0.50 per sq decimetere
Answers
Answer:
Totalexpenditure=Rs53.55
Step-by-step explanation:
\underline {\pink { Inner\:Dimensions \: of \: a \:wooden \:box: }}
InnerDimensionsofawoodenbox:
\begin{gathered} length (l) = 1\: m = 100\:cm , \\breadth (b) = 65\:cm \\Height (h) = 55\:cm \end{gathered}
length(l)=1m=100cm,
breadth(b)=65cm
Height(h)=55cm
Thickness \: of \: the \: box (w) = 2.5 \:cmThicknessofthebox(w)=2.5cm
\underline { \gray { Outer \: dimensions \:of \:the \:box :}}
Outerdimensionsofthebox:
L = l + 2w = 100\:cm + 5 \:cm = 105 \:cmL=l+2w=100cm+5cm=105cm
B = b + 2w = 65\:cm + 2\times 2.5 = 65+5 = 70\:cmB=b+2w=65cm+2×2.5=65+5=70cm
H = h + 2w = 55 + 5 = 60\:cmH=h+2w=55+5=60cm
\blue {Total \: surface \:area \:of \:the \:box }Totalsurfaceareaofthebox
\begin{gathered} = 2(LB+BH+HL) \\= 2(105\times + 70\times 60 + 60\times 105 )\\= 2(7350+4200+6300)\\= 2\times 17850 \\= 35700\:cm^{2} \\= 3.57 \:m^{2} \end{gathered}
=2(LB+BH+HL)
=2(105×+70×60+60×105)
=2(7350+4200+6300)
=2×17850
=35700cm
2
=3.57m
2
\begin{gathered} Cost \:of \: 1\:m^{2} \:surface \:area =Rs\: 15\\(Given) \end{gathered}
Costof1m
2
surfacearea=Rs15
(Given)
\begin{gathered} Cost \:of \: total \:surface \:Area = 15\times 3.75\\= Rs\:53.55 \end{gathered}
CostoftotalsurfaceArea=15×3.75
=Rs53.55
Therefore.,
\red { Total \: expenditure }\green {= Rs \:53.55}Totalexpenditure=Rs53.55