Question

A solid piece of metal in the form of cuboid of dimensions
24 cm x 18 cm x 4 cm is melted down and recasted into a cube.
Find the length of each edge of the cube.​

Answer 1

Answer:

$24 \times 18 \times 4 = 1728$

Volume of the cuboid

volume of cube=

${l}^{3}$

${l}^{3} = 1728$

l³=12

Answer 2

Given dimensions of the cuboid are 24 cm, 18 cm and 4 cm respectively.

❍ Let's say, the length of each edge of the cube be a cm.

$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$⠀⠀⠀⠀

To calculate the volume of cuboid Formula is given by :

$\bf{\dag}\;\underline{\boxed{\sf{ \: Cuboid_{ \: (volume)} = l \times b \times h \: }}}$

where,

• l is 24 cm
• b is 18 cm
• h is 4 cm

$\underline{\bf{\dag} \:\mathfrak{Substituting\;all\:the\;values\: :}}$⠀

⠀

$:\implies\sf Volume = l \times b \times h \\\\\\:\implies\sf Volume = 24 \times 18 \times 4 \\\\\\:\implies\sf Volume = 432 \times 4\\\\\\:\implies\underline{ \boxed{ \frak{ Volume = 17 28\;cm^3}}}$

⠀

$\therefore$ Needed Volume of the cuboid is 1728 cm³.

$\rule{250px}{.3ex}$

⠀

$\underline{\bigstar\:\boldsymbol{According \;to\; the\; given \;Question :}}$

⠀

• When the solid piece of metal in the form of cuboid of given dimensions is melted and converted into a cube.

⠀

Therefore,

⠀

$\dashrightarrow\sf Volume_{\;cuboid} = Volume_{\;cube}\\\\\\\dashrightarrow\sf 1728 = (a)^3 \\\\\\\dashrightarrow\sf \sqrt[3]{1728} = a \\\\\\\dashrightarrow\sf 12 = a \\\\\\\dashrightarrow\underline{\boxed{\frak{a = 12\:cm}}}\;\bigstar$

⠀

$\therefore{\underline{\textsf{Hence,\; length\;of\;each\;edge\;of\:cube\:is\; \textbf{12 cm }.}}}$