The length of a box is 36 cm. If you cut the length equally into 3 parts, the surface area will increase 120 cm^2. What is the volume of the box?

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Answer 1 · 2018-05-23T00:23:57

#1080cm^3#

so we cut the box in 3 parts each on is:

#(36 cm)/3 = 12 cm# long:

When we cut the box twice that adds 4 new surface areas, 2 at each cut that equal a total of 120 so each end will be:

#(120 cm^2)/4 = 30cm^2#

So now we have 3 boxes that are #12 cm# long with bases #30 cm^2#

#V_"box" = l*w*h#

#A_"base" = l*w#

putting these together:

#V_"box" =A_"base"*h#

#V_"box" =30cm^2*12cm = 360cm^3#

Finally since there are 3 boxes:

#3*360cm^3=1080cm^3#