Question

A cone is 8.4cm high and the radius of its base is 2.1cm . it is melt and recast into a sphere . the radius of the sphere is
(a ) 4.2cm.
(b) 2.1 cm.
(c )2.4cm.
(d) 1.6 cm.​

Answer 1

Correct option is

B

2.1 cm

Volume of the cone =

3

1

πr

c

2

h

Volume of the sphere =

3

4

πr

s

3

r

c

is the radius of cone =2.1 cm ....(Given)

Let r

s

be the radius of the sphere

h is the height of cone =8.4 cm ...(Given)

Volume of cone = Volume of sphere ...(Given)

⇒

3

1

πr

c

2

h=

3

4

πr

s

3

⇒

3

1

r

c

2

h=

3

4

r

s

3

⇒r

s

3

=9.261

⇒r

s

=2.1 cm