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# https://vle.mathswatch.co.uk/images/questions/question15493.png

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https://vle.mathswatch.co.uk/images/questions/question15493.png

Nov 4, 2017

#1
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surface area of cylinder  =  (circumference of base)(height) + 2(area of base)

surface area of cylinder  =  2 pi r h  +  2 pi r2               r  =  60/2  =  30    and    h = 4 * 60  =  240

surface area of cylinder  =  2 pi (30)(240)  +  2 pi (30)2

surface area of cylinder  =  14400pi + 1800pi   =   16200pi   ≈   50894 square mm

surface area of box  =  2LW + 2LH + 2HW

And  L = 60 + 60 = 120 mm ,  W = 60 + 60 = 120 mm ,  H = 60 mm

surface area of box  =  2(120)(120) + 2(120)(60) + 2(60)(120)

surface area of box  =  28800 + 14400 + 14400   =   57600 square mm

50894  is less than  57600 , so the cylinder has a smaller surface area.

Nov 4, 2017
edited by hectictar  Nov 5, 2017

#1
+1

surface area of cylinder  =  (circumference of base)(height) + 2(area of base)

surface area of cylinder  =  2 pi r h  +  2 pi r2               r  =  60/2  =  30    and    h = 4 * 60  =  240

surface area of cylinder  =  2 pi (30)(240)  +  2 pi (30)2

surface area of cylinder  =  14400pi + 1800pi   =   16200pi   ≈   50894 square mm

surface area of box  =  2LW + 2LH + 2HW

And  L = 60 + 60 = 120 mm ,  W = 60 + 60 = 120 mm ,  H = 60 mm

surface area of box  =  2(120)(120) + 2(120)(60) + 2(60)(120)

surface area of box  =  28800 + 14400 + 14400   =   57600 square mm

50894  is less than  57600 , so the cylinder has a smaller surface area.

hectictar Nov 4, 2017
edited by hectictar  Nov 5, 2017