Question

The radius of a solid metallic sphere is 8 cm the sphere is melted and recast into 8 equal solid spherical balls find the diameter of the balls

Answer 1

Answer:

Step-by-step explanation:

volume of big sphere=volume of 8 spheres

4/3πr^3=8*4/3πR^3

r^3=8*R^3

8*8*8=R^3*8

512/8=R^3

R^3=64

R=8

Answer 2

The diameter of the balls is 8 cm

Step-by-step explanation:

Radius of metallic sphere = 8 cm

Volume of sphere =$\frac{4}{3} \pi r^3 = \frac{4}{3} \pi (8^3)$

Volume of 1 spherical ball =$\frac{4}{3} \pi r^3$

Volume of 8 spherical ball =$8 \times \frac{4}{3} \pi r^3$

We are given that The radius of a solid metallic sphere is 8 cm the sphere is melted and recast into 8 equal solid spherical balls

So, Volume of sphere =Volume of 8 spherical balls

$\frac{4}{3} \pi (8^3)=8 \times \frac{4}{3} \pi r^3\\(8^3)=8 \times r^3\\\frac{8^3}{8}=r^3\\\sqrt[3]{\frac{8^3}{8}}=r\\4 = r$

Diameter of ball = 2r =2 (4)= 8 cm

Hence the diameter of the balls is 8 cm

#Learn more:

The radius of a solid metallic sphere is radius 8cm. The sphere is melted and recast into eight equal solid spherical ball. Determine the diameter of the balls.

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