What is the greatest surface area of a rectangle solid that can be build from 16 identical unit cubes?

Question

Answer = __________sq units

Answer 1

32

Answer 2

First of all its built not build.

Secondly, let's look at the possible answers.

The factors of 16 are {1,2,4,8,16}

A. A 1 x 16 x 1 rectangular solid has four faces containing 16 square units (1 x 16) each or 64 plus two faces with 1 square unit (1 x 1) each for a total of 66 square units.

B. A 2 x 8 x 1rectangular solid has two faces with 16 square units (2 x 8) each, two faces with 8 square units (1 x 8) each and two faces with 2 square units (1 x 2) each for a total of 52 square units.

C. A 4 x 4 x 1 rectangular solid has two faces with 16 square units (4 x 4) each and four faces with 4 square units (1 x 4) each, for a total of 48 square units.

D. A 2 x 2 x 4 rectangular solid has two faces of 4 square units (2 x 2) each and four faces of 8 square units (2 x 4) each for a total of 40 square units.

You should be able to take it from here.

Answer 3

16

Answer 4

40 sq units. Think of 8 cubes stacked across another 8 cubes.
That gives you 4 sides of 8 squ units, and another 4 on each end.
4 x 8 = 32
2 x 4 = 08
40

Answer 5

66 sq units

one long string of cubes makes for the least wasted space. Each of the 4 sides has an area of 16sq units plus 1 sq unit on each end.

Answer 6

66

Reason : If you put them all in one row there would be 14 cubes with 4 faces of surface area exposed and the other 2 would have 5 faces of surface area exposed.

Thus - (14x 4) + (2 x 5) = 56 + 10 = 66

Answer 7

64 sq units... I think

Edit: Argh! I forgot those 2 sides.

Answer 8

66 (I think!)

a rectangle 1x16 made by putting them all in a row

then it's 4x16 plus 2 (1 on each end!)

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