Question

12. The internal measurements of a box are 20 cm
long, 16 cm wide, and 24 cm high. How many
4 cm cubes could be put into the box? (ICSE)​

Answer 1

Answer:

According to the question, we are given a cuboidal box of dimensions 20 cm length, 16 cm, breadth and 24 cm height. We are asked to find the number of cubes of length 4 cm that can fit into the box.

The concept to be used here is the Volume of Cuboid Box is equal to the Volume of the Cubes.

Volume of Cuboid Box = 20 × 16 × 24 = 7680 cm³

Volume of 1 Cube = 4 × 4 × 4 = 64 cm³

Let the number of cubes fitting into the box be denoted as 'n'.

⇒ n × 64 = 7680 cm³

⇒ n = 7680 cm³ / 64 cm³

⇒ n = 120

There the number of cubes that can fit into the cuboidal box is 120.

Answer 2

Question :--- The internal measurements of a box are 20 cm long, 16 cm wide, and 24 cm high. How many 4 cm cubes could be put into the box?

Concept and Formula :--

→ Volume of box is in form of cuboid whose volume is = length * breadth * height .

→ Volume of cube = (side)³

→ Number of Box = (Volume or box ) / (volume of cube box )

________________________

Solution :--

putting values we get,

→ Volume of box = (20*16*24) cm³

→ volume of small cube box = (4*4*4)cm³

Hence, Number of box required =

(20*16*24)/(4*4*4)

= 7680/64

= 120 box .

Hence, 120 boxes of side 4cm will put into the box..