Question

Find the number of unit cubes in the following 3-D figures.

Answer 1

The number of unit cubes in the following 3-D figures.

$Basic formula for cubes = (number pf dots - 1)$

In Fig 1:

• In the given sheets dots are uniformly distributed.
• So on joing 2 adjacent dot within the given Isometric sheet a unit cube is obtained.
• In given fig 2 unit cube are placed in vertical position upon each other.
• Similarly in horizontal direction 3 unit cubes are place adjacent to every other.
• ∴ Total no of unit cubes in given figure are: 2+3 = 5

In Fig 2 :

• In each bar 3 dots are added which is able to form 2 unit cubes
• ∴ 2× 4(bars) = 8 unit cubes
• And 1 unit cube is at the middle joing all the 4 bars
• ∴ Total no. of unit cubes in given figure are: 8 + 1 = 9

In Fig 3 :

• On the highest layer 3 dots are joined.  
• Here, there are 4 unit cubes within the top layer
• In bottom layer, there are 4 + 12 = 16 unit cubes.
• ∴ Total no. of unit cubes in given figure are: 4+16 = 20

In Fig 4 :

• In Given fig, there's 1 cube at the highest
• In the middle layer, there are 4 cubes
• In the bottom layer, there are 9 cubes
• ∴ Total no. of cubes in given figure are: 1 + 4 + 9 = 14

Answer 2

answer

The number of unit cubes in the following 3-D figures.

Basic formula for cubes = (number pf dots - 1)Basicformulaforcubes=(numberpfdots−1)

In Fig 1:

In the given sheets dots are uniformly distributed.

So on joing 2 adjacent dot within the given Isometric sheet a unit cube is obtained.

In given fig 2 unit cube are placed in vertical position upon each other.

Similarly in horizontal direction 3 unit cubes are place adjacent to every other.

∴ Total no of unit cubes in given figure are: 2+3 = 5

In Fig 2 :

In each bar 3 dots are added which is able to form 2 unit cubes

∴ 2× 4(bars) = 8 unit cubes

And 1 unit cube is at the middle joing all the 4 bars

∴ Total no. of unit cubes in given figure are: 8 + 1 = 9

In Fig 3 :

On the highest layer 3 dots are joined.

Here, there are 4 unit cubes within the top layer

In bottom layer, there are 4 + 12 = 16 unit cubes.

∴ Total no. of unit cubes in given figure are: 4+16 = 20

In Fig 4 :

In Given fig, there's 1 cube at the highest

In the middle layer, there are 4 cubes

In the bottom layer, there are 9 cubes

∴ Total no. of cubes in given figure are: 1 + 4 + 9 = 14

I hope it help you in maths