Question

9) A rectangular block 6 cm by 12 cm by 15 cm is cut up in to an exact number of equal cubes. Find the least
possible number of cubes.
A. 10 B 20 C. 30 D. 40​

Answer 1

Answer:

Step-by-step explanation:

Given :-

Dimension of rectangular block = (6 × 12 × 15) cm

To Find :-

Least  possible number of cubes.

Formula to be used :-

Volume of the Block = L × B × H

Solution :-

Putting all the value, we get

⇒ Volume of the Block = L × B × H

⇒ Volume of the block = (6 x 12 x 15) cm³

⇒ Volume of the block =  1080 cm³.

Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm

H.C.F. of 6 cm, 12 cm, 15 cm = 3 cm

⇒ Volume of this cube = (3 x 3 x 3) cm³

⇒ Volume of this cube = 27 cm³.

⇒ Number of cubes = 1080/27

⇒ Number of cubes = 40.

Hence, the least  possible number of cubes are 40.

Answer 2

AnswEr :

• Dimensions of Rectangular Block is 6cm, 12cm and 15cm.
• Find Number of Cubes Made up by cutting that block.

• We will find the Volume of Block First :

⇒ Length × Breadth × Height

⇒ 6 cm × 12 cm × 15 cm

⇒ 1080 cm³

Now we will find largest possible side of cube which is going to be made of this block. We will find the HCF of Dimensions.

◗ 6 = 1 × 2 × 3

◗ 12 = 1 × 2 × 2 × 3

◗ 15 = 1 × 3 × 5

» HCF ( 6, 12, 15 ) = 3

Highest Common Factor of 6, 12 and 15 is 3 and i.e. the largest possible side of cube.

• We will find the Volume of Cube Now :

⇒ ( Side )³

⇒ ( 3 cm )³

⇒ ( 3 cm × 3 cm × 3 cm )

⇒ 27 cm³

_________________________________

⇝ No. of Cubes × Volume of Cube = Volume of Block

⇝ No. of Cubes × 27 cm³ = 1080 cm³

⇝ No. of Cubes = 1080 cm³ /27 cm³

⇝ No. of Cubes = 40

∴ Correct Option is [ D] 40 Possible Cubes