Question

Suppose the length and width of the box double. Does the surface area S double? Complete the explanation. (ignore the options i put at the bottom they were incorrect

Answer 1

No, the surface area didn't double. It more than doubled (closer to tripled).

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Step-by-step explanation:

• L = 24 = length
• W = 27 = width
• H = 10 = height

S = surface area of the box

S = 2*(LW + LH + WH)

S = 2*(24*27+24*10+27*10)

S = 2316 square cm

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Let's double the values of L and W

• L = 24 doubles to L = 48
• W = 27 doubles to W = 54
• Keep H = 10 the same as before.

Now let's recompute the surface area

S = 2*(LW + LH + WH)

S = 2*(48*54+48*10+54*10)

S = 7224 square cm

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Summary so far:

• The original box has surface area 2316 sq cm
• The larger box has surface area 7224 sq cm

Divide the larger value over the smaller to find that 7224/2316 = 3.119 approximately.

Since this result is not 2, it means the surface area did not double. It more than doubled. It would be more accurate to say the surface area roughly tripled.

Side note: if you were to double the length, width, and height, then the surface area would quadruple.