Question

A box is 1.8m long,90cm wide,60cm height. Soap cakes of measurements 6cm×4.5cm×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

Answer:

$\sf Length = 1.8m$

$\sf \pink \implies 180cm$

$\sf Breadth=90cm$

$\sf Height = 60cm$

$\sf Volume= l × b × h$

$\sf\blue \implies \green{180 \times 90 \times 60}$

$\sf\red \implies \orange{972000{cm}^{2}}$

$\sf Length \:of \:a \:soap\: cake = 6 cm$

$\sf Breadth \:of \:a \:soap \:cake = 4.5 cm$

$\sf Height \:of \:a \:soap\: cake = 40mm\\ \sf=4cm$

$\sf Volume\: of\: soap \:cake = 6 × 4.5 × 4{cm}^{3}$

$\sf\pink \implies \purple{108.0{cm}{3}}$

$\sf \green \therefore \blue{Required\: of \: soap\:cakes}$

$\sf \purple \implies \pink{\frac{volume \: of \: the \: box}{volume \: of \: one \: soap \: cake} }$

$\sf \orange \implies \red{ \cancel\frac{972000}{108}}$

$\sf \pink \implies \purple{9000}$

$\sf\green{Hence}$

$\sf \blue{9000 \: soap \: cakes \: can \: be \: packed \: in \: the \: box.}$

Answer 2

Answer:

$\sf Length = 1.8mLength=1.8m$

$\sf \pink \implies 180cm⟹180cm$

$\sf Breadth=90cmBreadth=90cm$

$\sf Height = 60cmHeight=60cm$

$\sf Volume= l × b × hVolume=l×b×h$

$\sf\blue \implies \green{180 \times 90 \times 60}⟹180×90×60$

$\sf\red \implies \orange{972000{cm}^{2}}⟹$$972000$

$\sf Length \:of \:a \:soap\: cake = 6 cmLengthofasoapcake =6 cm$

$\sf Breadth \:of \:a \:soap \:cake = 4.5 cmBreadthofasoapcake =4.5 cm$

$\begin{gathered}\sf Height \:of \:a \:soap\: cake = 40mm\\ \sf=4cm\end{gathered}$

Heightofasoapcake =40mm

=4cm

$\sf Volume\: of\: soap \:cake = 6 × 4.5 × 4{cm}^{3}Volumeofsoapcake=6×4.5×4cm </p><p>3$

$\sf\pink \implies \purple{108.0{cm}{3}}⟹108.0cm3$

$\sf \green \therefore \blue{Required\: of \: soap\:cakes}∴Requiredofsoapcakes$

$\sf \purple \implies \pink{\frac{volume \: of \: the \: box}{volume \: of \: one \: soap \: cake} }⟹$

volumeofonesoapcake

volumeofthebox

$\sf \orange \implies \red{ \cancel\frac{972000}{108}}⟹$

108

972000

$\sf \pink \implies \purple{9000}⟹9000$

$\sf\green{Hence}Hence$

$\sf \blue{9000 \: soap \: cakes \: can \: be \: packed \: in \: the \: box.}$