Question

A hollow sphere of internal and external diameter 4 cm and 8 cm respectively is melted into a shape of a cylinder of base circumference 88 cm. find the height of the cylinder.

Answer 1

Given,

Internal diameter of hollow sphere d=4 cm

External diameter of hollow sphere D=8 cm

Diameter of circular base of cone d

c

=8 cm

Hence,

Internal radius of hollow sphere r=

2

d

=2 cm

External diameter of hollow sphere R=

2

D

=4 cm

Radius of circular base of cone r

c

=

2

d

c

=4 cm

Volume of hollow sphere V=

3

4

π(R

3

−r

3

)

And volume of cone V=

3

1

πr

c

2

h

Given that hollow sphere is melted into the cone

→volume of hollow sphere = volume of cone

3

4

π(R

3

−r

3

)=

3

1

πr

c

2

h

Hence, hight of cone is given by

h=

3×π×r

c

2

3×4×π×(R

3

−r

3

)

h=

r

c

2

4×(R

3

−r

3

)

h=

4

2

cm

2

4×(4

3

−2

3

) cm

3

h=

16

4×(64−8)

cm

h=

16

4×56

cm

h=

16

224

cm

h=14 cm