Question

How many cubes each of side 3cm can be made from a cuboid whose dimensions are 21cm × 27cm × 8cm ?​

Answer 1

SoLuTion:

We know that,

• Volume of cube = a³
• Volume of cuboid = lbh

Given that,

• Length of cuboid = 21 cm
• Breadth of cuboid = 27 cm
• Height of cuboid = 8 cm

Applying the values,

$\bigg{\twoheadrightarrow}\sf{\;Volume\;of\;cube=3^3}\\ \\ \\\bigg{\twoheadrightarrow}\sf{\;Volume\;of\;cube=3\times3\times3}\\ \\ \\\bigg{\twoheadrightarrow}\sf{\;Volume\;of\;cube=3\times9}\\ \\ \\\bigg{\twoheadrightarrow}\sf{\;Volume\;of\;cube=27\;cm^3}$

Now,Volume of cuboid,

$\bigg{\twoheadrightarrow}\sf{\;Volume\;of\;cuboid=lbh}\\ \\ \\\bigg{\twoheadrightarrow}\sf{\;Volume\;of\;cuboid=21\times27\times8}\\ \\ \\\bigg{\twoheadrightarrow}\sf{\;Volume\;of\;cuboid=567\times8}\\ \\ \\\bigg{\twoheadrightarrow}\sf{\;Volume\;of\;cuboid=4536\;cm^3}$

Then,

$\sf{No.of.cube\;made=\frac{Volume\;of\:cuboid}{volume\;of\;cube}}\\ \\ \\ \sf{No.of.cube\;made=\frac{4536}{27}}\\ \\ \\ \sf{No.of.cube\;made=168}\\ \\ \\ \\\therefore\sf{Hence,168\;cube\;can\;be\;made\;by\;cuboid}$