Question

a solid metal cone of radius 6cm is melted and shaped to from a solid sphere of radius 3cm find the height of the cone​

Answer 1

Answer :

Given :

Radius of the cone = 6 cm

Radius of the sphere is 3 cm

Required to find :

1. Height of the cone

Solution :

In the question it is given that a solid metal cone of radius 6 cm is melted and shaped to form of a solid sphere of radius 3 cm

The above statement actually says that the Volume of the cone is equal to Volume of the sphere .

So, using this we are going to solve this problem .

But , First we have to find the volume of the sphere.

Hence we have to use the formula for finding the volume of sphere

That is,

Volume of Sphere = 4/3πr^3

As we know that radius of the sphere is 3cm

So , substitute the respective values

Volume of sphere = 4/3 x 3.14 x 3 x 3 x 3. ( π = 3.14 or 22/7 )

= 113.04 cm^3

Therefore,

Volume of the sphere = 113.04 cm^3

As we know that,

Volume of the sphere = Volume of the cone = 113.04cm^3

Hence,

Volume of the cone = 113.04cm^3

to solve this we should also know about the formula of volume of the cone

Volume of the cone = 1/3πr^2h

radius of the cone = 6cm

so,

equal the values

1/3πr^2h = 113.04cm^3

1/3 x 3.14 x 6 x 6 x h = 113.04

3.14 x 2 x 6 x h = 113.04

37.68 x h = 113.04

h = 113.04 / 37.68

h = 3 cm

Therefore,

Height of the cone = 3cm

Answer 2

Answer:

into means multiply.

Step-by-step explanation: The   volume of a sphere= 4/3 pi r cube

the volume of cone = 1/3 pi r square multiply  height

as both of the sphere and cone are made from same volume of metal

the volume of both will be same .

as cone formula needs height ..we are going to use sphere formula

4/3 pi r cube= 4/3 into  pi  [ 3.142] multiply by 3 cube [ 3 into 3 into 3]

which is equal to 113.09 [ round off]

so.. cone volume = 113.09 = 1/3 into pi into r square into height

we do not  know height so let it be x

113.09 = 1/3 into pi [3.142] into 6 square into x

133.09 = 37.7 [ I multiplied all except x] into x

x= 133.09/ 37.7 ... which is = 3.53 cm .. so cone height = 3.53

I HEARTFULLY HOPE IT HELPS

PLS MARK ME AS BRAINLIEST