Question

long, 8 m wide and 10 m high.
6. The volume of a wooden plank is 33,750 cu. cm. If cuboidal pieces measuring
30 cm in length, 15 cm in width and 5 cm in height have to be cut from the
wooden plank, how many pieces of cuboids can be cut from it?​

Answer 1

$\sf Given \begin{cases} & \sf{Volume\:of\:wooden\:plank = \bf{33750\:cm^3}} \\ & \sf{Length\:of\:cuboidal\: pieces = \bf{30\:cm}} \\ & \sf{Breadth\:of\:cuboidal\: pieces = \bf{30\:cm}} \\ & \sf{Height\:of\:cuboidal\:pieces = \bf{5\:cm}} \end{cases}$

To find: Number of pieces that can be cut from Wooden Plank?

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☯ Let number of cuboidal pieces be n.

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$\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}$

$:\implies\sf Volume_{\:(wooden\:plank)} = n \times Volume_{\:(cuboidal\:piece)}\\ \\ \\ :\implies\sf 33750 = n \times \bigg\lgroup 30 \times 15 \times 5 \bigg\rgroup\\ \\ \\ :\implies\sf 33750 = n \times 2250\\ \\ \\ :\implies\sf n = \cancel{ \dfrac{33750}{2250}}\\ \\ \\:\implies{\underline{\boxed{\frak{\purple{n = 15}}}}}\;\bigstar$

$\therefore\:{\underline{\sf{Thus,\:20\:cuboidal\:pieces\:can\:be\;cut\:from\:wooden\:plank.}}}$

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$\qquad\qquad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}$

• $\sf Volume\:of\:cuboid = l \times b \times h$

• $\sf Total\:surface\:area\:of\:cuboid = 2(lb + bh + hl)$

• $\sf Curved\:surface\:area\:of\:cuboid = 2(l + b)h$

• $\sf Diagonal\:of\:cuboid = \sqrt{l^2 + b^2 + h^2}$

Answer 2

Answer:

$\huge \frak {Given}$

• Volume of park = 33,750 cm³
• Length of cuboidal pieces =30 cm
• Breadth of cuboidal pieces = 15 cm
• Height of cuboidal pieces = 5 cm

$\huge \frak{To \: Find}$

Total pieces

$\huge \frak{Solution}$

Let the total cuboid be x

Firstly we will find volume of cuboidal box.

$\bf \red{Volume \: = l \times b \times h}$

$\tt \mapsto \: Volume = 30 \times 15 \times 5$

$\tt \mapsto \: Volume = 150 \times 15$

$\tt \mapsto Volume = 2250 \: {cm}^{3}$

$\bf x = \dfrac{33750}{2250}$

$\mathfrak \red{x \: = 15}$

Hence :-

15 boxes are required

Learn More :-

• Area of circle = πr²
• Area of rectangle = length × Breadth
• Volume of cube = side³
• TSA of cuboid = 2(lb + bh + lh)