Increase in Surface Area? (CEMC)

Geometry Level 3

A cube measures 10 × 10 × 10 10 \times 10 \times 10 . Each side is measured in cm. Three cuts are made parallel to the faces of the cube as shown creating eight separate solids which are then separated. What is the increase in the total surface area?

500 c m 2 500\ cm^2 100 c m 2 100\ cm ^2 300 c m 2 300\ cm^2 600 c m 2 600 \ cm^2 200 c m 2 200\ cm ^2

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Marta Reece
Jun 27, 2017

Every small cube has three new faces and three old faces, so the overall area has doubled.

The original area was 10 × 10 × 6 = 600 c m 2 10\times10\times6=600\ cm^2

so the increase is aslo 600 c m 2 \boxed{600\ cm^2} .

Or you could calculate the area of one of the small cubes as 5 × 5 × 6 = 150 c m 2 5\times5\times6=150\ cm^2

get the area of all of them as 8 × 150 = 1200 c m 2 8\times150=1200\ cm^2

and subtract the original 600 c m 2 600\ cm^2 , to get the answer 600 c m 2 600\ cm^2

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Thank you.

Hana Wehbi - 3 years, 11 months ago

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