Question

How many cuboidal shaped chalks each of volume 8cm³can be packed in a box measuring 12cm *7cm *2cm?​

Answer 1

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Q) How many cuboidal shaped chalks each of volume 8 cm³ can be packed in a box measuring 12cm×7cm×2cm ?

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❁ Analysis :

• In this question , we have to simply find the volume of the box and divide it by the volume of a chalk .

• The dimension of the box is given so, we would simply multiply to get it's volume .

• The final answer would be Unitless as , it is the "number" of items to be found .

$\bf{Given}\begin{cases}\sf{Volume \;of \; a \; chalk=\bf{8cm^2}} \\ \sf{Dimension\;of\;box=\bf{12cm×7cm×2cm}}\\ \sf{\bf{Chalks} \:are \:to \:be \:packed\:in \:\bf{box}}\\ \sf{The \;box\;is\;\bf{cuboidal}.}\end{cases}$

❁ To Find :

• The number of chalks that can be packed in the box.

❁ Solution :

We know ,

• ${\rm{Length_{box}\;(l)=12cm}}$
• ${\rm{Breadth_{box}\;(b)=7cm}}$
• ${\rm{Height_{box}\;(h)=2cm}}$

So,

$\rm \mapsto \: volume _{box} = lbh$

$\mapsto \rm \: volume _{box} = 12cm \times 7cm \times 2cm \\ \\ \leadsto \: \underline{ \boxed{ \pink{ {\rm volume _{box}}= \red{ \rm168 {cm}^{3} }}}}$

And,

$\leadsto \: \underline{ \boxed{ \rm{ \purple{volume _{chalk} = \red{8 {cm}^{3} }}}}}$

So ,

$\mapsto \rm \: no. \: of \: chalks \: that \: can \: be \: packed = \frac{volume \: of \: box}{volume \: of \: a \: chalk}$

$\rm \mapsto \rm \: no. \: of \: chalks = \cancel{ \frac{168 \: {cm}^{3} }{8 \: {cm}^{3} } }$

$\leadsto \large \boxed{ \boxed{ \sf{ \red{no. \: of \: chalks = 21}}}}$

So,

21 chalks can be packed in the box with the given dimensions.

Answer 2

${\underline{\underline{\bf{Given:}}}}$

• Dimensions of a box: Length = 12 cm, Breadth = 7 cm and Height = 2 cm.
• Volume of a cuboidal shaped chalk= 8 cm³.

${\underline{\underline{\bf{Need\:to\:find:}}}}$

• The number is chalks that can be packed inside the box.

${\underline{\underline{\bf{Formula\:to\:be\:used:}}}}$

$\underline{\boxed{\sf{{Volume}_{(cuboid)}=lbh\:cu.units}}}$

$\sf{Where,}$

• l = length
• b = breadth
• h = height

${\underline{\underline{\bf{Solution:}}}}$

The number of chalks that can be packed inside a cuboidal box can be found by dividing the volume of the box by the volume of a chalk. Here, according to our question, the volume of a chalk is given and the dimensions of the box are given. So, first we have to find the volume of the cuboid, and next we will be able to find the required answer. Let's do it !!

★ Volume of the box:

By substituting the given measures in the formula,

$\:\:\:\:\:\:\:\implies{\sf{Length\times Breadth\times Height\:cu.units}}$

$\:\:\:\:\:\:\:\implies{\sf{12\times 7\times 2}}$

$\:\:\:\:\:\:\:\implies{\sf{84\times 2}}$

$\:\:\:\:\:\:\:\implies{\sf{\underline{168\:{cm}^{3}}}}$

Now, we know the volume of the cuboid, so let's proceed with the next step.

★ Number of chalks that can be packed:

$\:\longrightarrow{\boxed{\sf{\frac{Volume\:of\:box}{Volume\:of\:a\:chalk}}}}$

$\:\:\:\:\:\:\:\implies{\sf{\cancel{\frac{168}{8}}}}$

$\:\:\:\:\:\:\:\implies{\underline{\underline{\sf{\red{21}}}}}$

${\underline{\underline{\bf{Final\: answer:}}}}$

• 21 chalks can be packed inside the box of given dimensions.

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