Question

Dimensions of a cuboid is length is 6 cm, breadth is 5cm and height is 4 cm. How many cubes each of side 2 cm can be cut from it?

Answer 1

$\sf\large\underline{Given:}$

• $\rm{Cubiod\:_{length}=6cm}$
• $\rm{Cubiod\:_{breadth}=5cm}$
• $\rm{Cubiod\:_{height}=4cm}$
• $\rm{Cube\:_{each\:side}=2cm}$

$\sf\large\underline{To\: Find:}$

• $\rm{Number\:_{cube}=?}$

$\sf\large\underline{Solution:}$

• At first calculate the volume of cubiod and cube than divide]

$\sf\large\underline{Formula\: Used:}$

$\tt{\implies V\:_{cubiod}=l\times\:b\times\:h}$

$\tt{\implies V\:_{cube}=S^3}$

• Calculate volume of cubiod]

$\tt{\implies V\:_{cubiod}=6\times\:5\times\:4}$

$\tt{\implies V\:_{cubiod}=120\:cm^3}$

• Calculate volume of cube]

$\tt{\implies V\:_{cube}=2^3}$

$\tt{\implies V\:_{cube}=8\:cm^3}$

$\sf\large{Hence,}$

$\rm{\implies Number\:_{cube}=\frac{V\:_{cubiod}}{V\:_{cube}}}$

$\rm{\implies Number\:_{cube}=\dfrac{120}{8}}$

$\rm{\implies Number\:_{cube}=15\:cube}$

Answer 2

Answer:

⋆ DIAGRAM :

$\setlength{\unitlength}{0.68cm}\begin{picture}(12,4)\linethickness{0.3mm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\qbezier(6,6)(4,7.3)(4,7.3)\qbezier(6,9)(4,10.2)(4,10.3)\qbezier(11,9)(9.5,10)(9,10.3)\qbezier(11,6)(10,6.6)(9,7.3)\put(8,5.5){\sf{6 cm}}\put(4,6.3){\sf{5 cm}}\put(10,7.5){\sf{4 cm}}\end{picture}\setlength{\unitlength}{0.65cm}\begin{picture}(2,3)\thicklines\put(2,6){\line(1,0){3.3}}\put(2,9){\line(1,0){3.3}}\put(5.3,9){\line(0,-1){3}}\put(2,6){\line(0,1){3}}\put(0,7.3){\line(1,0){3.3}}\put(0,10.3){\line(1,0){3.3}}\put(0,10.3){\line(0,-1){3}}\put(3.3,7.3){\line(0,1){3}}\put(2,6){\line(-3,2){2}}\put(2,9){\line(-3,2){2}}\put(5.3,9){\line(-3,2){2}}\put(5.3,6){\line(-3,2){2}}\put(3.4,5.5){\sf2 cm}\put(0,6.3){\sf2 cm}\put(5.5,7.5){\sf2 cm}\end{picture}$

$\rule{120}{0.8}$

Concept : Whenever we cut Solid Shapes and reshape to some other Solid Shape. Then Volume of Shape Never Change.

⠀

$\underline{\bigstar\:\textsf{According to the Question :}}$

$:\implies\sf Volume_{(Cuboid)}=Volume_{(Cube)} \times Number\\\\\\:\implies\sf (L \times B \times H)=(Side)^3 \times Number\\\\\\:\implies\sf (6 \:cm \times 5 \:cm \times 4 \:cm) = (2 \:cm)^3 \times Number\\\\\\:\implies\sf (5 \times 24) \:cm^3 = 8 \:cm^3 \times Number\\\\\\:\implies\sf \dfrac{(5 \times 24) \:cm^3}{8\:cm^3} = Number\\\\\\:\implies\sf 5 \times 3 = Number\\\\\\:\implies\underline{\boxed{\sf Number = 15}}$

⠀

$\therefore\:\underline{\textsf{Hence, \textbf{15} cubes can be cut from cuboid}}.$