Question

Twenty seven solid iron spheres, each of radius r and surface area S are melted to
form a sphere with surface area S'. Find the
(1) radius r' of the new sphere, (ii) ratio of S and S'.
How much

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Answer 1

3. Twenty seven solid iron spheres, each of radius r and surface area S are melted to
4. form a sphere with surface area S'. Find the
5. (1) radius r' of the new sphere, (ii) ratio of S and S'.
6. How much

Answer 2

Answer:

(i) Radius of 1 solid iron sphere =r

⇒Volume =

3

4

πr

3

⇒Volume of 27 solid iron spheres =27×

3

4

πr

3

⇒

3

4

πr

′

3

=27×

3

4

πr

3

r

′

3

=2πr

3

⇒r

′

=3r

(ii) Surface area =4πr

2

SA r

′

=4πr

′

2

=4π(3r)

2

=36πr

2

S

′

S

=

36πr

2

4πr

2

=

9

1

=1:9