Consider eight, eight-cubic centimeter (8 cm3) sugar cubes stacked so that they form a single 2 x 2 x 2 cube. How does the surface area of the single, large cube compare to the total surface area of the individual eight cubes? Report your answer as a ratio.

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ShsvettyClandy ShsvettyClandy

17-10-2016
Mathematics

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Consider eight, eight-cubic centimeter (8 cm3) sugar cubes stacked so that they form a single 2 x 2 x 2 cube. How does the surface area of the single, large cube compare to the total surface area of the individual eight cubes? Report your answer as a ratio.

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Anonymous Anonymous · Answer 1 · 2016-10-21T18:34:13-04:00

I have my solution here but just change the measurement into 8cm^3

Each face of a 1cm³ cube measures 1cm x 1cm; so the surface area (SA) of 1 face = 1cm².

A cube has 6 faces.

The SA of a 1cm³ cube is therefore 6 x 1cm² = 6cm²

The total SA of 8 cubes = 8 x 6cm² = 48cm²
_________________________

When arranged into a 2x2x2 cube, the new SA is that of the outer faces only.

Each outer face of a 2cm x 2cm x 2cm cube measures 2cm x 2cm; so the surface area of 1 face = 4cm².

The cube has 6 faces. So the SA is 6 x 4cm² = 24cm²
___________________

So the ratio
(SA of large cube):(SA of 8 indidivual cubes)
= 24:48
= 1:2

I hope my answer has come to your help. Thank you for posting your question here in Brainly.