Question

number of cuboid of dimensions 8 cm × 15 cm × 20 cm stacked together to form a cube is​

Answer 1

Number of cuboids with dimensions 8cm × 15cm × 20cm stacked together to form cube is​ 90

Given:

• Cuboids with dimensions 8cm × 15cm × 20cm
• Stacked together to form cube

To Find:

• Number of cuboids

Solution:

Step 1:

Prime factorize 8 , 15 and 20

8 = 2 * 2 * 2

15 = 3 * 5

20 = 2 * 2 * 5

Step 2:

Multiply 8 , 15 and 20 and make group of 3

2 * 2 * 2 * 3 * 5  * 2 * 2 * 5

= (2 * 2 * 2) * ( 2 * 2) * ( 3) * ( 5 * 5)

Step 3:

Note the factors required to make it perfect cube are

2 * 3 * 3 * 5

= 90

Number of cuboids with dimensions 8cm × 15cm × 20cm stacked together to form cube is 90

Answer 2

$Volume \: of \: Cuboid = L×B×H$

$= 8cm × 15cm × 20cm$

$= 2400 \: cm$

$L.C.M \: of \: 8,15 \: and \: 20 \: are \: 120$

$Volume \: of \: Cube \: wil \: be =l×b×h$

$=120 × 120 ×120$

$=1,728,000$

$= \frac{Volume of Cube }{Volume of Cuboid}$

$= \frac{1,728,000}{2400}$

$= 720$