Question

A solid cuboid of dimensions 8cm*4cm*2cm is melted and cast into identical cubes of edge 2cm. How many cubes will be made.

Answer 1

$\huge\mathtt{\pink{ANSWER:-}}$

8 cubes formed

$\huge\bold{\underline{SOLUTION:-}}$

$\bold{Given}\begin{cases}\sf{Dimensions \:of\: cuboid}\\ \sf{which\:is\:melted}\\ \sf{side\:of\:cube\:2cm}\end{cases}$

1st find the volume of cuboid

The formula to find the volume of cuboid

is Length ×Breadth×Height

$\bold{\underline{\red{According\:To\: Question:-}}}$

$\bold{\purple{Volume of cuboid=L\times B\times H}}$

$\bold{Given}\begin{cases}\sf{L=8cm}\\ \sf{b=4cm}\\ \sf{h=2cm}\end{cases}$

Now :-

$\sf Volume= 8cm\times 4 cm\times 2\\ \\ \sf\implies Volume\:of\: cuboid=32cm{}^{2}×2cm\\ \\ \sf\implies Volume\:of\: cuboid=64cm{}^{2}$

The volume of cuboid is $\tt 64cm{}^{3}$

It's melted to form a cube of edge 2cm

Now :-

$\bold{\purple{Volume\:of\:cube=side{}^{3}}}$

$\bold{Given}\begin{cases}\sf{Side\:cube=2cm}\end{cases}$

Volume of cube=side×side+side

Or $\tt side{}^{3}$

$\sf volume\:of\:cube=(2cm){}^{3}\\ \\ \sf\leadsto Volume=8cm{}^{2}$

$\bold{Volume\:of\:cube=8cm{}^{3}}$

$\bold{\blue{Volume\:Of\: cuboid=64cm{}^{3}}}$

Number of cubes formed by the cuboid is

$\bf\implies \frac{volume\:of\: cuboid}{volume\:cube}$

$\sf\implies number\:of\:cubes\:formed=\cancel{\frac{64}{8}}=8\\ \\ \sf\implies Number \:Of\:cubes\:formed=8$

#BAL

#Answerwithquality

Answer 2

THARA BHAI BABANDER

Step-by-step explanation:

TERA KO INTANA MARAGA KISHINA SOCHI NA HOGI