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

Answer:

90 in²

shoebox:

• volume = 64 in³

• surface area = 160 in²

Another shoebox:

• volume = 27 in³

• surface area = x in²

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$\sf (\dfrac{area1}{area2})^3 = (\dfrac{volume1}{volume2} )^2$

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$\sf \hookrightarrow (\dfrac{x}{160})^3 = (\dfrac{27}{64} )^2$

$\sf \hookrightarrow \dfrac{x^3}{160^3} = \dfrac{27^2}{64^2}$

$\sf \hookrightarrow \ x^3 = \dfrac{729*4096000}{4096}$

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

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

$\sf \hookrightarrow \ x = 90$