Question

Dimensions of a cuboid are 60 cm × 54 cm × 30 cm. How many cubes of side 6 cm can be placed in the cuboid

Answer 1

Question:

Dimensions of a cuboid are 60 cm × 54 cm × 30 cm. How many cubes of side 6 cm can be placed in the cuboid

Solution:

Let there be n no.of cubes in the cuboid

Implies,

volume of cuboid=n×volume of cube

$\implies \: \boxed{ \sf{n = \frac{volume \: of \: cuboid \: }{volume \: of \: cube} }}$

★Cuboid

Volume=l×b×h

Here,

l=60cm,b=54cm and h=30cm

Volume would be:(60×54×30)cm³

★Cube:

Side=6cm

Volume=s³=6³=(6×6×6)cm³

Substituting the values,

$\sf{n = \frac{(54 \times 60 \times 30)cm {}^{3} }{(6 \times 6 \times 6)cm {}^{3} } } \\ \\ \implies \: \sf{n =5 \times 9 \times 10 } \\ \\ \implies \: \boxed{\sf{n = 450}}$

There are 450 cubes in the cuboid

Answer 2

$\mathfrak{\underline{\underline{\huge{\red{Answer:-}}}}}$

450 Cubes

$\mathfrak{\large{\underline{\underline{\blue{\star{Explanation:-}}}}}}$

Cuboid :-

length = 60 cm

breadth = 54 cm

height = 30 cm

Volume of cuboid = l × b × h

» 60 × 54 × 30

» 97200 cm³

Cube :-

let a is side of cube

a = 6 cm

Volume of cube = a³

» a³ = 6³

» a = 216 cm³

$\rule{200}{2}$

Now,

Number of Cubes = Volume of Cuboid/Volume of Cube

» 97200 cm³/216cm³

» 450

$\rule{200}{2}$

So, 450 cubes can be placed in cuboid.