Question

A box is $1.8m$ long, $90cm$ wide, $60cm$ height. Soap cakes of measurements $6cm\times 4.5cm\times 40mm$ are to be packed in the box, so that no space is left. Find how many cakes can be packed in each box?

Answer 1

Length of the box $\left(l\right)=1.8m=180cm$
Breadth of the box $\left(b\right)=90cm$
Height of the box $\left(h\right)=60cm$
Volume of the box $=l\times b\times h$
$=180\times 90\times 60c{m}^3$
$=972000c{m}^3$
Length of a soap cake $=6cm$
Breadth of a soap cake $=4.5cm$
Height of a soap cake $=40mm=4cm$
Volume of one soap cake $=6\times 4.5\times 4c{m}^3$
$=108.0c{m}^3$
$\therefore$ Required number of soap cakes
$=\frac{\text{Volume of the box}}{\text{volume of one soapcake}}$
$=\frac{972000}{108}$
$=9000$
Hence, $9000$ soap cakes can be packed in the box.