Unit Cubes 3 – $5 \times 5$ Edges

Probability Level 1

If someone painted the outside of a $5 \times 5 \times 5$ cube made out of $1 \times 1 \times 1$ unit cubes, how many unit cubes would have paint on exactly 2 sides?

The answer is 36.

5 solutions

Sharky Kesa
May 23, 2014

For any $n \times n \times n$ cube, the rule for the number of cubes with 2 sides painted is $12(n-2)$ . If we apply this to the cube in question, we get $12(5-2)$ which has a value of 36.

i cant understand the question

Kazmeen Safdar - 6 years, 7 months ago

What if they asked for 3 sides, were we gonna ans this like 12(n-3) ? pls ans.... this.

Shawon Pathan - 5 years, 9 months ago

Nope, if they ask for 3 sides, we just answer 8 because a cube has 8 corners (which only can be painted on 3 sides)

Minh Nguyễn - 5 years, 8 months ago

Now i get the concept

Herbert Josephy - 1 year, 8 months ago

Is it a formula? How and where did you get such a formula??

Dibyojyoti Bhattacharjee - 8 months ago

Yoyo Jiang
Nov 16, 2014

Look at the picture. Each edge of the cube has 3 cubes that have paint on exactly 2 sides. There are 12 edges. 3 x 12 = 36

Scott Immel
May 24, 2014

A cube has 12 edges, thus it would have n-2 cubes painted for each edge, so f(n)=12(n-2).

f(5)=12(5-2)-12*3=36

Dishita Meshtru
Aug 1, 2020

$1 \times 1 \times 1$ cubes having 2 sides as a surface =12( number of cubes at the edge - number of cubes at the corner)

why 12? = there are 12 edges in a cube

= 12(5 - 2) = $12 \times 3$

= 36 cubes

Krishna Garg
Jun 8, 2014

Each TWO side of Cube will have 12 unit cube pained on two sides,remainin 3 sides( out of six will be three times that is 36 Ans. K.K.Garg,India

Unit Cubes 3 – 5 × 5 5 \times 5 5 × 5 Edges

The answer is 36.

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Unit Cubes 3 – $5 \times 5$ Edges