Question

4. If 60 identical cubical boxes can be fit into
a box of dimensions 20 m x 15 m x 25 m.
Find the dimensions and the volume of each
cubical box.
please give the write answer
​

Answer 1

Step-by-step explanation:

ANSWER

Volume of the cuboid =L×B×H

volume of the cuboid =60×54×30

volume of the cuboid =97200 cm

3

volume of the cube =a

3

volume of the cube =6×6×6

volume of the cube =216 cm

3

No of cubes that can be fitted =

volume of cube

volume of cuboid

=

216

97200

=450

Answer 2

$\large{\underline{\underline{\textsf{\maltese\: {\red{Given :-}}}}}}$

☉ Dimension of box = 20m × 15m × 25m

☉ Number of cubical boxes to be fitted = 60

$\large{\underline{\underline{\textsf{\maltese\: {\red{To Find :-}}}}}}$

☉ Length of edge of the each cubical box = ?

☉ Volume of each cubical box = ?

$\large{\underline{\underline{\textsf{\maltese\: {\red{Diagram :-}}}}}}$

$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines \qbezier(0,0)(0,0)(2,3) \qbezier(2,3)(2,3)(6,3) \qbezier(6,3)(6,3)(4,0) \qbezier(0,0)(0,0)(4,0) \qbezier(4,0)(4,0)(4,-3) \qbezier(0,0)(0,0)(0,-3) \qbezier(0,-3)(0,-3)(4,-3) \qbezier(4,-3)(4,-3)(6,0)\qbezier(6,0)(6,0)(6,3) \put(0.2,2){\bf15 m} \put(4.3,1.5){\bf 15m}\put(3,3.1){\bf20 m} \put(2,0.1){\bf 20m} \put(3,-1.4){\bf25 m} \put(-.9,-1.4){\bf 25m} \put(10,0){\framebox(1,1)} \put(11.2,0.4){\Large\bf x 60} \qbezier(9.8,0.4)(6,4)(2,0.3) \put(2,.3){\vector(-1,-1){.4}} \put(7.3,-3.5){\framebox(2.7,.7)} \put(7.35,-3.3){\bf@ BeBrainliest}\put(10.1,1.101){\bf5 m} \end{picture}$

$\large{\underline{\underline{\textsf{\maltese\: {\red{Solution :-}}}}}}$

Let the dimension of each cubical box of ‘a m’.

❄️ Volume of cube = Side³

⇒ Volume of 1 cubical box = (a m)³

⇒ Volume of 1 cubical box = a³ m³

❄️ Volume of cuboid = Length × Breadth × Height

Volume of the box = 20m × 15m × 25m

According to the Question,

$\textsf{ \dfrac{\textsf{Volume of the box}}{\textsf{Volume of 1 cubical boxes}} = 60}$

⇒ $\dfrac{\textsf{20m * 15m * 2m}}{\sf{a^3 m^3}} = 60$

⇒ $\sf \dfrac{\textsf{20 * 15 * 2}}{a^3} = 60$

⇒ $\dfrac{\textsf{20 * 15 * 2}}{60} = \sf a^3$

⇒ 125 = a³

⇒ $\displaystyle \sqrt[3]{125}$ = a

⇒ 5 = a

∴ a = 5m

∴ The length of the edge of the each cubical box is 5m.

❄️ Volume of cube = Side³

⇒ Volume of 1 cubical box = (5m)³

⇒ Volume of 1 cubical box = 125m³

∴ The volume of each cubical box is 125m³.