Question

how many cubes of side 3cm each can be cut from wooden block in the form of a cuboid whose length,breadth and height are 21cm,9cm and 8cm respectively. How much of wood is wasted?

Answer 1

Volume of cuboid = l.b.h = 21 x 9 x 8 = 1512 cubic cm

Volume of cube = a.a.a = 3 x 3 x 3 = 27 cubic cm

Total cubes carved can be = 1512/27 = 56

Answer 2

$\bf ➯length \: of \: the \: cuboid \: = 21cm$

$\bf ➯breadth \: of \: the \: cuboid \: = 9cm$

$\bf ➯height \: of \: cuboid= 21 \times 9 \times 8$

$➾5121cm$

$\bf ➯number \: of \: cubes \: that \: can \: be \: cut$

$\bf along \: the \: length \: = \cancel \dfrac{12}{3}$

$➾7$

$\bf ➯number \: of \: cubes \: that \: can \: be \: cut$

$\bf along \: the \: breadth \: = \cancel \dfrac{9}{3}$

$➾3$

$\bf ➯number \: of \: cubes \: that \: can \: be \: cut$

$\bf along \: the \: height \: = \dfrac{8}{3}$

$➾2.6$

$\bf ➯along \: the \: height \: we \: can \: be \: cut \:$

$\bf only \: 2 \: pieces \: and \: remaining \: is$

$\bf waste$

$\therefore \bf \: total \: number \: of \: cubes \: cut \:$

$⇒7 \times 3 \times 2$

$⇒42$

$\bf ➯volume \: of \: each \: cube \:$

$⇒3 \times 3 \times 3$

$⇒27 {cm}^{2}$

$\bf ➯volume \: of \: all \: cubes$

$⇒27 \times 42$

$⇒1134 {cm}^{2}$

$\therefore \bf \: volume \: of \: the \: waste \: wood$

$⇒1512 - 1134$

$➺378 {cm}^{2}$

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