Question

A metallic sphere of radius 10.5 cm is melted and then recast into small cones, each of radius 3.5 cm and height 3 cm. The number of such cones is

पर्याय

• 63

• 126

• 21

• 130

Answer 1

Radius of metallic sphere = 10.5 cm

Therefore,

Volume of the sphere

`=4/3pir^3`

`=4/3 xx pi xx 10.5 xx 10.5 xx 10.5`

`= (4630.5pi)/3            ................(1)`

Now,

Radius of the cone = 3.5 cm

and Height of the cone = 3 cm

Therefore,

Volume of the cone 

`=1/3 pir^2 h`

`=1/3 xx pi xx 3.5 xx 3.5 xx 3`

`=(36.75pi)/3           .......... (2)`

Number of cone = `"volume of sphere"/ "volume of cone"`

Dividing eq. (1) and (2) we get

Number of cone `= ((4630.5 pi)/3)/((36.75 pi)/3) = 126`

Number of cone = 126