Question

a right circular metallic cone of height 2.7 cm of radius of its base is 1.6 cm.it is melted and recast to form a sphere. find the radius of the sphere formed?​

Answer 1

Answer :

Given -

• Height of the cone = 2.7 cm
• Radius of its base = 1.6 cm
• The cone is melted and recast to form a sphere

To Find -

• Radius of the sphere ?

Solution -

Volume of a cone = ⅓πr²h.

So, Volume = ⅓*3.14*2.7²*1.6

⇒ ⅓*3.14*7.29*1.6

⇒ ⅓*3.14*11.66

⇒ 36.62/3

⇒ 12.20 cm³

Now, as the melted and recast to form a sphere, the volume of the cone will be equal to the volume of the sphere.

So, 4/3*π*r³ = 12.20 cm³

⇒ 4/3*3.14*r³ = 12.20 cm³

⇒ 12.56/3*r³ = 12.20 cm³

⇒ 4.18*r³ = 12.20

⇒ r³ = 12.20/4.81

⇒ r³ = 2.91

⇒ r = 1.427

Hence, the Radius of the sphere = 1.427 cm.

Answer 2

Given :

• Height of the cone = 2.7 cm
• Radius of its base = 1.6 cm

_________________________

To Find :

• Radius of sphere formed.

_________________________

Solution :

We know the formula to calcu;te the volume of cone.

⇒Volume = 1/3πr²h

⇒Volume = 1/3 * 22/7 * 1.6 * 1.6 * 2.7

⇒Volume = 1/3 * 22/7 * 11.66

⇒Volume = 256.52/21

⇒Volume = 21.21 cm³

$\rule{200}{2}$

Now,

⇒Volume of cone = Volume of sphere

⇒ 4/3 *π * r³ = 12.21

⇒ 4/3 * 22/7 * r³ = 12.21

⇒4.19 * r³ = 12.21

⇒r³ = 12.21/4.19

⇒r³ = 2.91

⇒ r = 1.427