Question

the radius of a solid iron sphere is 8cm.eight rings of iron plate of external radius 20/3cm and tckness 3cm are made by melting their sphere.find the internal diameter of each ring

Answer 1

Solution :-

Radius of the iron sphere = 8 cm

External radius of the 8 rings of iron plates = 20/3 cm

Thickness of the 8 rings of iron plates 3 cm

Let internal radius of the ring be r cm

Volume of the sphere = 4/3πr³

⇒ 4/3*22/7*8*8*8

⇒ 45056/21

= 2145.52 cm³

Now, it can be assumed that each ring of iron plate is a hollow cylindrical shell having internal radius 'r' cm and external radius 20/3 cm along with the  height 3 cm

Volume of each ring = π*(R² - r²)h

⇒ 3π*[(20/3)² - (r)²]

⇒ Volume of 8 rings = 8*3π[(20/3)² - (r)²]

⇒ 24π*[(20/3)² - (r)²]

Now, volume of sphere = Volume of 8 iron rings

⇒ 2145.52 = 24π[(20/3)² - (r)²]

⇒ 2145.52 = 24*22/7(400/9 - r²)

⇒ 2145.52*7 = 528(400/9 - r²)

⇒ 15018.64/528 = 400/9 - r²

⇒ r² = 44.44 - 28.44

⇒ r² = 16

⇒ r = √16

⇒ r = 4 cm

So, internal radius of the each ring is 4 cm.

Then, diameter = 4*2 

= 8 cm

Answer.

Answer 2

Answer:

Step-by-step explanation:

Radius of the iron sphere = 8 cm

External radius of the 8 rings of iron plates = 20/3 cm

Thickness of the 8 rings of iron plates 3 cm

Let internal radius of the ring be r cm

Volume of the sphere = 4/3πr³

⇒ 4/3*22/7*8*8*8

⇒ 45056/21

= 2145.52 cm³

Now, it can be assumed that each ring of iron plate is a hollow cylindrical shell having internal radius 'r' cm and external radius 20/3 cm along with the  height 3 cm

Volume of each ring = π*(R² - r²)h

⇒ 3π*[(20/3)² - (r)²]

⇒ Volume of 8 rings = 8*3π[(20/3)² - (r)²]

⇒ 24π*[(20/3)² - (r)²]

Now, volume of sphere = Volume of 8 iron rings

⇒ 2145.52 = 24π[(20/3)² - (r)²]

⇒ 2145.52 = 24*22/7(400/9 - r²)

⇒ 2145.52*7 = 528(400/9 - r²)

⇒ 15018.64/528 = 400/9 - r²

⇒ r² = 44.44 - 28.44

⇒ r² = 16

⇒ r = √16

⇒ r = 4 cm

So, internal radius of the each ring is 4 cm.

Then, diameter = 4*2  

= 8 cm

Answer.

Hope it help u :))