Question

A cuboid is of dimensions (60*50*30)cm.How many small cubes with side 6 cm can be placed in the given cuboid?

Answer 1

$\huge{\bf{\green{\mathfrak{Question:-}}}}$

• A cuboid is of dimensions (60*50*30)cm.How many small cubes with side 6 cm can be placed in the given cuboid?

$\huge {\bf{\orange{\mathfrak{Answer:-}}}}$

• $\textsf{Dimensions of the cuboid = 60 cm, 50 cm and 30 cm.}$

• $\boxed{\sf Volume \: of \: the \: cuboid \: = \: lbh \: units^{3}.}$

• $\sf 60 \: * \: 50 \: * \: 30$

• $\boxed{\sf 90,000 \: units^{3}.}$

• $\textsf{Dimensions of the cube = 6 cm.}$

• $\boxed{\sf Volume \: of \: the \: cube \: = \: s^{3} \: units^{3}.}$

• $\sf 6^{3}$

• $\boxed{\sf 216 \: units^{3}.}$

• $\textsf{Number of Cubes that can be placed in the cuboid =}$

• $\sf \dfrac{Volume \: of \: cuboid}{Volume \: of \: cube}$

• $\sf \dfrac{90,000}{216}$

• $\sf 416 \: cubes.$

$\huge{\bf{\red{\mathfrak{Conclusion:-}}}}$

• $\boxed{\therefore{\sf Number\: of\: Cubes\: that\: can\: be \:placed\: in \:the \:cuboid\: = \: 416.}}$

$\huge{\bf{\purple{\mathfrak{Note:-}}}}$

• Actually, when we divide the volumes of cuboid and cube we get 416.66.

• $\textsf{This means that some area is left out.}$

• $\textsf{Area left out =}$

• $\sf Volume \:of \:cuboid\: - \:(Volume\: of\: cube\:* \:416)$

• $\sf 90,000 \:- \:(216\: *\: 416)$

• $\sf 90,000\: - \:89,856$

• $\sf 144 \:cm^{2} \:of \:area\: is \:left \:out.$

Answer 2

$\Large{\bf{Given\::}}$

• Dimensions of a cuboid is (60 × 50 × 30) cm.

That means,

• Length = 60 cm

• Breadth = 50 cm

• Height = 30 cm

$\\ \Large{\bf{To\: Find\::}}$

• No. of small cubes placed in the given cuboid, with side 6 cm.

$\\ \Large{\bf{Solution\::}}$

As we know that,

➣ Volume of a cuboid is,

$\orange\bigstar\:{\Large\mid}\:\bf\blue{Volume_{(cuboid)}\:=\: Length\times{Breadth}\times{Height}\:}\:{\Large\mid}\:\green\bigstar$

➠ Volume = (60 × 50 × 30) cm³

➠ Volume = 90000 cm³

Again,

➣ Volume of a cube is,

$\orange\bigstar\:{\Large\mid}\:\bf\purple{Volume_{(cube)}\:=\:(Side)^3\:}\:{\Large\mid}\:\green\bigstar$

Where,

• Side of the cube is 6 cm.

➠ Volume = 6³

➠ Volume = 6 × 6 × 6

➠ Volume = 216 cm³

Now,

$\orange\bigstar\:{\huge\mid}\:\bf\red{No.\:of\:cubes\:=\:\dfrac{Vol^m\:of\: cuboid}{Vol^m\:of\:1\:cube}}\:{\huge\mid}\:\green\bigstar$

$:\implies\:\tt{No.\:of\:cubes\:=\:\dfrac{90000}{216}\:}$

$:\implies\:\tt{No.\:of\:cubes\:=\:416.66\:\approx\:416}$

$:\implies\:\bf\pink{No.\:of\:cubes\:=\:416}$

∴ 416 small cubes placed in the given cuboid.