Question

A shoebox has a volume of 64 in.³ and a surface area of 160 in.² what is the surface area of a similar shoe box if its volume is only 27 in.³ show your work or explain how you got your answer

Answer 1

90 in²

shoebox:

• volume = 64 in³

• surface area = 160 in²

Another shoebox:

• volume = 27 in³

• surface area = x in²

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`\sf ((area1)/(area2))^3 = ((volume1)/(volume2) )^2`

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`\sf \hookrightarrow ((x)/(160))^3 = ((27)/(64) )^2`

`\sf \hookrightarrow (x^3)/(160^3) = (27^2)/(64^2)`

`\sf \hookrightarrow \ x^3 = (729*4096000)/(4096)`

`\sf \hookrightarrow \ x^3 = 729000`

`\sf \hookrightarrow \ x = \sqrt[3]{729000}`

`\sf \hookrightarrow \ x = 90`