Question

A carpenter has to make cubical wooden toys of side 20 cm each. How many cubical toys can be made from a log of wood of size 3m by 80 cm by 50 cm? A) 100 B) 150 C) 160 D) 200​

Answer 1

$\large\underline{\underline{\red{\pmb{\sf{ \: Given :-}}}}}$

• The side of the cubical wooden toy is 20 cm each. How many cubical toys can be made from a log of wood with dimensions 3m ,80 cm and 50 cm.

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$\large\underline{\underline{\blue{\pmb{\sf{ \: To \: Find :-}}}}}$

• How many cubical toys could be made .

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$\large\underline{\underline{\orange{\pmb{\sf{ \:Solution :-}}}}}$

~ Formula Used :

$\large{\orange{\bigstar}} \: \: \: {\underline{\boxed{\red{\sf{ Volume{\small_{(Cuboid)}} = L \times W \times H}}}}}$

$\large{\orange{\bigstar}} \: \: \: {\underline{\boxed{\red{\sf{ Volume{\small_{(Cube)}} = Side³}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━}$

~ Calculating the Volume of log :

Here :

• ↠ L = Length = 3 m or 300 cm
• ↠ W = Width = 80 cm
• ↠ H = Height = 50 cm

Let's Calculate :

${\dashrightarrow{\qquad{\sf{ Volume{\small_{(Log)}} = L \times W \times H}}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Volume{\small_{(Log)}} = 300 \times 80 \times 50}}}} \\ \\ \ {\qquad{\sf{ Volume \: of \: Log \: = {\pink{\sf{1200000 \: cm}}}}}}$

~ Calculating the Volume of toys :

Here :

• ↠ Side = 20 cm

Let's Calculate :

${\dashrightarrow{\qquad{\sf{ Volume{\small_{(Cubical \: box)}} = Side³}}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Volume{\small_{(Cubical \: Box)}} = 20³}}}} \\ \\ \ {\dashrightarrow{\qquad{\sf{ Volume{\small_{(Cubical \: Box)}} = 20 \times 20 \times 20 }}}} \\ \\ \ {\qquad{\sf{ Volume \: of \: Cubical \: box \: = {\green{\sf{ 8000 \: cm}}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━}$

~ Cubical toys could be made :

${\qquad{\longmapsto{\sf{ No. \: of \: toys{\small_{(Made)}} = \dfrac{Vol. \: of \: log}{Vol. \: of \:toy}}}}} \\ \\ \ {\qquad{\longmapsto{\sf{ No. \: of \: toys{\small_{(Made)}} = \dfrac{1200000}{8000}}}}} \\ \\ \ {\qquad{\longmapsto{\sf{ No. \: of \: toys{\small_{(Made)}} = \cancel\dfrac{1200000}{8000}}}}} \\ \\ \ {\qquad{\sf{ Toys \: could \: be \: Made \: = {\color{maroon}{\sf{ 150 }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━}$

Therefore :

❝ 150 toys could be made using the log . ❞

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Answer 2

Given,

A carpenter has to make cubical wooden toys of side $20$$cm$ each

We have to find how many cubical toys can be made from a log of wood of size $3mby80cmby50cm$

First we have to convert meters into centimeters

$1m =100cm$

So,

$3 m = 300cm$

We have to find the volume of cubical wooden toys of side $20cm$ each

Volume $= l\times b\times h$

$= 20\times20\times20\\=8000$

Now,

Find the volume of $300cm,80cm,50cm$

$v=300\times80\times50$

$v=1200000$

Now,

We have to find the how many cubical toys can be made from a log of wood of size $3m\times80cm\times50cm$

S0, divide $1200000$ and $8000$

$=\frac{1200000}{8000}\\=150$

Therefore, $150$ cubical toys can be made from a log of wood size  $3mby80cmby50cm$.