Question

The symmetrical solid shown in the image is made of small unit cubes. What fraction of cubes have atleast one face visible if you are the observer?
​

Answer 1

Question :- The symmetrical solid shown in the image is made of small unit cubes. What fraction of cubes have atleast one face visible if you are the observer ?

Answer :-

→ Total Number of cubes in Top part = 2 * 3 = 6 .

→ Total Number of cubes in Middle part = 4 * 3 = 12 .

→ Total Number of cubes in Bottom Part = 6 * 3 = 18.

So,

→ Total Number of cubes in the Solid = 6 + 12 + 18 = 36.

Now,

→ Number of cubes whose atleast one face visible in Top part = 6 .

→ Number of cubes whose atleast one face visible in Middle part = 3(Front) + 3(Right side) = 6 .

→ Number of cubes whose atleast one face visible in Bottom part = 3(Front) + 5(Right side) = 8 .

Therefore,

→ Total Number of cubes whose atleast one face visible = 6 + 6 + 8 = 20 .

Hence,

→ Required Fraction = (Total Number of cubes whose atleast one face visible) / (Total Number of cubes in the Solid)

→ Required Fraction = (20/36)

→ Required Fraction = (5/9) (Ans.)