Question

A metallic solid cylinder of 14 cm diameter and 32 cm height is melted into 77 solid cubes of
equal size, then the edge of each cube must be​

Answer 1

Answer :-

Edge of each cube must be 4 cm.

Explanation :-

Diameter of the solid cylinder (d) = 14 cm

So Radius of the solid cylinder (r) = d/2 = 14/2 = 7 cm

Height of the solid cylinder (h) = 32 cm

Volume of the solid cylinder = πr²h

= (22/7) * 7² * 32

= (22 * 7 * 32 )

Let the edge of each solid cube be 'a' cm

Volume of each solid cube = a³ cm³

Volume of 77 solid cubes. 77(a³) = 77a³ cm³

Given

Solid cylinder is casted into 77 solid cubes of equal size

i.e Volume of solid cylider = Volume of 77 solid cubes

⇒ 22 * 7 * 32 = 77a³

⇒ (22 * 7 * 32)/77 = a³

⇒ (22 * 32)/11 = a³

⇒ (2 * 32) = a³

⇒ 64 = a³

⇒ 4³ = a³

⇒ 4 = a

⇒ a = 4

∴ the edge of each cube must be 4 cm.

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Edge of each must be 4 cm

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explanation:}}}$

Given :-

• Diameter of the metallic cylinder is 32 cm
• Height of the metallic cylinder is 32 cm

To find :-

• The edge of 77 solid cubes formed by melting the metallic cylinder.

Solution :-

Since, the metallic cylinder is melted to form 77 solid cubes the volume of the both shapes will be equal.

$\bold{Volume\:of\:cylinder\:=\:\pi\:r^2h}$

Where, r = radius of the cylinder

h = height of the cylinder

So, first we will calculate the radius of the cylinder.

$\implies$ $\bold{Radius\:=\:\frac{Diameter}{2}}$

$\implies$ $\bold{Radius\:=\:\frac{14}{2}}$

Radius of the cylinder = 7 cm

Now block in the values in the formula for volume of a cylinder,

$\implies$ $\bold{\frac{22}{7}\times\:7^2\times\:32}$

$\implies$ $\bold{\frac{22}{7}\times\:7\times\:7\:\times\:32}$

$\implies$ $\bold{22\times\:7\:\times\:\times\:32}$

$\implies$ $\bold{154\times\:32}$

$\implies$ $\bold{4928}$ -----> (1)

•°• Volume of cylinder = 4928 cm³

Mentioned above when a particular shape is melted and given a new shape, the volume of the initial shape is equal to the volume of the shape formed after melting.

Let the edge of the cube be x

$\bold{Volume\:of\:a\:cube\:x^3}$

So as per the statement, we can write,

${\bold{\boxed{Volume\:of\:cylinder\:=\:Volume\:of\:cube}}}$

Number of solid cubes formed is 77

$\implies$ $\bold{4928\:=\:77x^3}$ ---> From (1)

$\implies$ $\bold{\frac{4928}{77}}$ = $\bold{x^3}$

$\implies$ $\bold{64}$ = $\bold{x^3}$

$\implies$ ³√64 = $\bold{x}$

$\implies$$\bold{4\:=\:x}$