Question

A solid metal cube of side 6 cm is recast into a
solid sphere. Find the radius of the sphere.​

Answer 1

Answer:
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Answer 2

Given:

• Cube side = 6 cm
• Cube into solid sphere

To Find:

• Radius of the sphere.?

Formula Used:

$\bigstar{\underline{\boxed{\sf{ \green{Volume_{(Cube)} } = a^3 }}}}$

$\bigstar{\underline{\boxed{\sf{ \blue{Volume_{(Sphere)} } = \dfrac{4}{3} πr^3 }}}}$

Solution:

volume of the cube;

$\implies$ a³

$\implies$ 6³

$\implies$ 6 × 6 × 6

$\implies$ 216 cm³

Hence,

• The Volume of the cube is 216 cm³.

Now, Solid Cube converted into solid sphere so Volume of Cube is equal to Volume of Sphere.

Volume of Cube = Volume of Sphere

216 cm³ ( Cube ) = 216 cm³ ( Sphere )

After substituting values;

$\implies$ 4/3 πr³

$\implies$ 216 = 4/3 πr³

$\implies$ 216 = 4/3 × 22/7 × r³

$\implies$ 216 × 3 × 7/ 4 × 22 = r³

$\implies$ 51.5 = r³

$\implies$ r = ³√51.5

$\implies$ r = 3.7 cm

Therefore,

• The Radius of the sphere is 3.7 cm.