Question

10. A solid cube of edge 14 cm is melted down
and recast into smaller and equal cubes each
of edge 2 cm. Find the number of smaller
cubes obtained.​

Answer 1

Answer:

343

Step-by-step explanation:

Volume of 1 cube =( side )^3

= 14^3

=2744 cm^3

Volume of 2 cube = 2^3

= 8 cm^3

No. of cubes = 2744÷8

= 343

Hope this helps

Answer 2

Given:-

• Edge of original cube = 14cm
• Edge of melted cubes = 2cm each

To find:-

• Number of smaller cubes obtained on melting the original cubes.

Solution:-

Edge of original cube = 14cm

We know,

$\sf{Volume\: of \:a \:cube = (side)\times (side)\times (side) = {(side)}^{3}\: cubic \: units}$

Therefore,

$\sf{Volume = {(14)}^{3}\:{cm}^{3}}$

= $\sf{Volume = 2744 {cm}^{3}}$

Now,

Edge of small cubes = 2cm

$\sf{Volume = {(2)}^{3}\:{cm}^{3}}$

= $\sf{Volume = 8 \: {cm}^{3}}$

Now, To find the number of small cubes obtained we need to divide the volume of original cube by the volume of small cubes.

Therefore,

$\sf{Number\:of\:small\:cubes\:formed = \dfrac{Volume\:of\:original\:cube}{Volume\:of\:small\:cube}}$

= $\sf{Number\:of\:small\:cubes\:formed = \dfrac{2744}{8}}$

= $\sf{Number\:of\:small\:cubes\:formed = 343}$

Important Formulas to know:-

• $\sf{Volume\: of \:cube = {(side)}^{3} \:cubic\:units}$
• $\sf{Lateral\: Surface \: Area\: of\: a \: cube = 4{a}^{2} \: square\:units}$
• $\sf{Total\:Surface\:Area\:of\:cube = 6{a}^{2} \: square\:units}$
• $\sf{Volume\:of\:cuboid = (length \times breadth \times height)\: cubic\:units}$
• $\sf{Lateral\:Surface\:Area\:of\:Cuboid = 2(length + breadth)\times height \:sq. units}$
• $\sf{Total\:surface\:area\:of\:cuboid = 2(lb + b h + h l) sq. units}$
• Where l = length, b = breadth and h = height.