Question

if a cube of side 22cm is melted and recast to form a sphere what will be the radius of the sphere?

Answer 1

Answer:

Step-by-step explanation:

volume of cube =volume of sphere

  a^3                   =            4/3πr^3

      22^3             =           4/3πr^3

      10648            =        4/3πr^3

          2662         =           1/3*22/7*r^3

           121            =        1/3*1/7*r^3

     121                 =         1/21 * r^3

           121*21      =      r^3

            2541     =        r^3

∛2541                =        r

13.65             =      r

r                  =13.65 cm....

Answer 2

The radius of the sphere is "13.65 cm".

Step-by-step explanation:

Given,

The side of cube = 22 cm

To find, the radius of the sphere = ?

Let the radius of the sphere = r

Volume of the cube = Volume of the sphere

 ∴ $a^3=\dfrac{4}{3} \pi r^3$

⇒ $22^3=\dfrac{4}{3} \times \dfrac{22}{7} r^3$

⇒ $22^2=\dfrac{4}{3} \times \dfrac{1}{7} r^3$

⇒ $484=\dfrac{4}{3} \times \dfrac{1}{7} r^3$

 ⇒ $121=\dfrac{1}{3} \times \dfrac{1}{7} r^3$

 ⇒  $r^3=121\times 21=2541$

 ∴ r = 13.65 cm

Hence,  the radius of the sphere is 13.65 cm.