Question

27 solid iron spheres each of radius r and surface are S melted to form a square with square area s find the (i) Radius r2 of the new sphere (ii) Ratio if S and S'​

Answer 1

Answer:

Let the radius =r

Surface area=S

Whenever one shape melted to another shape

So,

Volume of 27 sphere of radius r=volume of big sphere of radius r

′

Now,

27×(

3

4

πr

3

)=

3

4

π(r

′

)

3

⇒27r

3

=(r

′

)

3

On solving then,

r

′

=3r

So,

Ratio of S and S

′

S

′

S

=

4π(r

′

)

2

4πr

2

=

(r

′

)

2

r

2

=

(3r)

2

r

2

=

9

1

Answer 2

Step-by-step explanation:

(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