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A metallic sphere of radius 10.5 cm is m...

A metallic sphere of radius 10.5 cm is melted and then recast into smaller cones, each of radius 3.5 cm and height 3 cm. How many cones are obtained ?

A

136

B

126

C

146

D

156

Text Solution

Verified by Experts

The correct Answer is:
B
`"Radius of the sphere, "R=21/2cm`.
`"Volume of the sphere "=4/3piR^(3)=(4/3pixx21/2xx21/2xx21/2)cm^(3)`
`=((3087pi)/2)cm^(3)`.
Radius of the cone, `r=7/2cm.`
`"Height of each cone, "h=3 cm.`
`"Volume of each cone"=1/3pir^(2)h=(1/3pixx7/2xx7/2xx3)cm^(3)`
`=((49pi)/4)cm^(3)`
`:." required number of cones"=("volume of the sphere")/("volume of each cone")`
`=((3087pi)/2xx4/(49pi))=126.`
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