Question

A block of wood measuring 12cm by 16 cm by 8cm is cut into cubical blocks of the same size . Find the number of cubical blocks if each side measures 4cm.
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Answer 1

Answer :-

• Number of blocks required is 24 blocks.

Step-by-step explanation :

To Find :-

• The number of cubical blocks.

Solution :-

Given that,

• Side of a cubical box = 4cm

Dimensions of the cuboidal wood = 12cm*16cm*8cm.

• Length = 12cm
• Breadth = 16cm
• Height = 8cm

Hence, the volume of cuboidal wood, As we know that,

Volume of cuboid = lbh,

Where,

• l = Length
• b = Breadth
• h = Height

=> Volume = l × b × h

=> 12cm × 16cm × 8cm

=> ( 12 × 16 × 8 ) cm³

=> ( 192 × 8 ) cm³

=> 1536 cm³

The volume of cubical block, As we know that,

Volume of cube = a³,

Where,

• a = side of cube

=> Volume = a × a × a

=> 4cm × 4cm × 4cm

=> ( 4 × 4 × 4 ) cm³

=> ( 16 × 4 ) cm³

=> 64cm³

Now, the number of cubical blocks. As we know that,

Number of blocks = Volume of cuboid ÷ Volume of cube,

=> 1536 ÷ 64

=> 24.

Hence,

• Number of blocks required is 24 blocks.

Answer 2

$\large{\underbrace{\underline{\bf{Required~Answer:-}}}}$

$\frak{Given}\begin{cases}\sf{Dimensions\:of\:block=\bf{12cm}\:by\:\bf{16cm}\:by\bf{8cm.}}\\\sf{Side\:of\:a\:cubical\:block=\bf{4cm.}}\end{cases}$

$\bigstar\:\underline{\textit{\textbf{To\:Find:}}}$

• Number of cubical block that can be made.

$\star\;\underline{\textit{\textbf{Solution:}}}$

» We would first find the volume of the wooden block.

» Then we would find the volume of the cubical block.

» Then we would divide the volume of wooden block by the volume of the cubical block so as to get the answer.

◆ Finding the Volume of wooden block -

• Length = 16 cm
• Breadth = 12 cm
• Height = 8 cm

» Using the formula to find the volume of a cuboid.

$\odot \: \boxed{ \sf \: Volume _{ \: Cuboid} = Length \times Breadth \times Height}$

So,

$\colon \rarr \sf \: Volume _{ \: (Wooden \: Block)} = 16 \times 12 \times 8 \: {cm}^{3} \\ \\ \colon \dashrightarrow \underline{ \boxed{ \pink{ \frak{Volume _{ \: (Wooden \: Block)} =1536 \: {cm}^{3} }}}}$

◆ Finding the Volume of cubical block -

• Side of the cubical block = 4 cm.

» Using the formula to find the volume of cube.

$\odot \: \boxed{ \sf{Volume _{ \: Cube} = {side}^{3} }}$

So,

$\colon \rarr \sf \: Volume _{ \: (Cubical \: Block)} = {(4 \: cm)}^{3} \\ \\ \colon \rarr \sf \: Volume _{ \: (Cubical \: Block)} = 4 \times 4 \times 4 \: {cm}^{3} \\ \\ \colon \dashrightarrow \underline{ \boxed{ \pink{ \frak{Volume _{ \: (Cubical \: Block)} = 64 \: {cm}^{3}}}}}$

◆ Finding the number of blocks -

$\colon \leadsto \sf \: No. \: of\: blocks = \frac{Volume \: of \: Wodden \: block}{Volume \: of \: cubical \: block} \\ \\ \colon \leadsto \sf \: No. \: of \: block = \cancel \frac{1536 \: {cm}^{3} }{64 \: {cm}^{3} } \\ \\ \colon \dashrightarrow \underline{ \boxed{ \bf{ \red{No. \: of \: blocks = 24}}}}$

$\therefore\;\underline{\sf Number \;of \;Cubical\;blocks\;formed=\bf{24.}}$