Question

. A metal block having sides 10 cm, 15 cm, 30 cm has cut into equal cubes. If the block is exhausted completely what will be the least possible number of cubes?

Answer 1

Answer:

Step-by-step explanation HCF (10,15,30)=5

10/5=2, 15/5=3 , 30/5= 6

Therefore no. Of cubes 2×3×6=36 cubes.

Same method can use for such questions.

-SHASHIRAJ

Answer 2

The least possible number of cubes is  36 if A metal block having sides 10 cm, 15 cm, 30 cm has cut into equal cube and  block is exhausted completely

Given:

• A metal block having sides 10 cm, 15 cm, 30 cm
• Cut into equal cubes
• The block is exhausted completely

To Find:

• The least possible number of cubes

Solution:

• Volume of cuboid =length x breadth x height
• Volume of cube = (side)³

Step 1:

To find least numbers of cube , size of cube should be maximum

for that Need to find HCF of Side length (10 , 15 , 30)

10 = 2 x 5

15 = 3 x 5

30 = 2 x 3 x 5

HCF = 5

Hence Maximum possible size of cube = 5 x 5 x 5

Step 2:

Calculate the volume of metal block

= 10 x 15 x 30

= 4500 cm³

Step 3:

Calculate the volume of each cube cut

= 5 x 5 x 5

= 125  cm³

Step 4:

Calculate the number of cubes

4500 / 125

= 36

Hence the least possible number of cubes is  36