Question

11 How many cubic blocks of wood of side 20 cm can be cut from a block of wood having dimensions
2 m, 80 cm, and 40 cm?
9.​

Answer 1

${\frak{Cuboidal_{\;(wood\;block)}}} \begin{cases} & \text{Length = 2 m = \bf{200\;cm}} \\ & \text{Breadth = \bf{80\;cm} } \\ & \text{Height = \bf{40\;m}} \end{cases}$

$\dag\;{\frak{\underline{We\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Volume_{\;(cuboid)} = l \times b \times h}}}}$

$\qquad\qquad:\implies\sf 200 \times 80 \times 40$

$\qquad\qquad:\implies{\underline{\boxed{\frak{\purple{64000\;cm^3}}}}}\;\bigstar$

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☯ Side of cubic blocks = 20 cm

$\dag\;{\frak{\underline{We\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Volume_{\;(cube)} = a^3}}}}$

$\qquad\qquad:\implies\sf 20 \times 20 \times 20$

$\qquad\qquad:\implies{\underline{\boxed{\frak{\purple{800\;cm^3}}}}}\;\bigstar$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━

☯ Now, We have to find no. of cubic blocks formed from cuboidal block.

$\qquad:\implies\sf No.\;of\;boxes = \dfrac{Volume\;of\;cuboidal\;block}{Volume\;of\;cubic\;block}$

$\qquad\qquad:\implies\sf No.\;of\;boxes = \dfrac{64000}{800}$

$\qquad\qquad\qquad:\implies{\underline{\boxed{\frak{80\;boxes}}}}\;\bigstar$

$\therefore\;\sf \underline{80\;cubical\;boxes\;formed\;from\;a\; cuboidal\;block.}$