stack of cubes

Geometry Level 3

Shown in the above figure is a stack of cubes standing on a horizontal ground. The blue cube has an edge length of 30 cm \text{30 cm} , the green cube has an edge length of 20 cm \text{20 cm} , the purple cube has an edge length of 16 cm \text{16 cm} and the red cube has an edge length of 11 cm \text{11 cm} . What is the total area of the visible portion in cm 2 \text{cm}^2 ?. Give your answer as the sum of its digits.


The answer is 21.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

5 ( 3 0 2 ) − 2 0 2 + 5 ( 2 0 2 ) − 1 6 2 + 5 ( 1 6 2 ) − 1 1 2 + 5 ( 1 1 2 ) = 7 , 608 5(30^{2})-20^{2}+5(20^{2})-16^{2}+5(16^{2})-11^{2}+5(11^{2})=7,608

Answer : 21 \boxed{21}

Note : Literally taken, the "visible" portion actually has an area of 4,254 c m 2 cm^{2} , leaving an answer of 15 15 . I would rephrase the question.

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Actually, the "visible" portion would be less than 4,254 cm^2.

A Former Brilliant Member - 3 years, 2 months ago

It is unclear whether "visible" includes the base. Or is it visible from just one point? If so, which point?

Interestingly, if the base is included, the area comes to 8508, which has the same sum of digits, so the result comes out as correct.

Marta Reece - 3 years ago

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