Question

A godown measures 40m x 25m x 10m. find the maximum number of crates that can be accommodated in the godown if each crate measures 1.5m x 1.25m x 0.5m.

Answer 1

No. of Wooden Crates = Volume of Godown/Volume of 1 Crate

⇒ No. of Wooden Crates = (Length × Breadth × Height)/Volume of 1 Crate

⇒ No. of Wooden Crates = (40 m × 25 m × 15 m)/(Length × Breadth × Height)

⇒ No. of Wooden Crates = (40 × 25 × 15 m³)/(Length × Breadth × Height)

⇒ No. of Wooden Crates = (15000 m³)/(1.5 m × 1.25 m × 0.5 m)

⇒ No. of Wooden Crates = (15000 m³)/(1.5 × 1.25 × 0.5 m³)

⇒ No. of Wooden Crates = (15000 m³)/(0.9375 m³)

⇒ No. of Wooden Crates = 15000/0.9375

⇒ No. of Wooden Crates = 150000000/9375

⇒ No. of Wooden Crates = 16000

Answer 2

Solution :

Given :

Godown dimensions:

• Length = 40 m ,
• breadth = 25 m
• and height = 10 m

Diagram :

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\put(8,5.5){40 \:m}\put(4,6.3){25 \:m}\put(11.2,7.5){10 \:m}\end{picture}$

Crate Dimensions :

• Length = 1.5 m ,
• breadth = 1.25 m
• and height = 0.5 m

Diagram :

$\setlength{\unitlength}{0.74 cm}\begin{picture}(12,4)\thicklines\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\put(8,5.5){1.5 \: m}\put(4,6.3){1.25 \: m}\put(11.2,7.5){0.5 \:m}\end{picture}$

Volume of Godown

= length × breadth × height

$\sf = (40 \times 25 \times 10)m {}^{3}$$\sf = 10000m {}^{3}$

Volume of wooden crate

= length × breadth × height

$\sf = (1.5 \times 1.25 \times 0.5)m {}^{3}$$\sf = 0.9375m {}^{3}$

Number of wooden crates

$\sf\:=\dfrac{Volume\:of\: Godown}{Volume\:Of\:1\:Crate}$

$\sf = \dfrac{10000}{9375} \times 10000$

$\sf = 10666.66$

Therefore, 10666 wooden crates can be stored in the godown.