The volume of a sphere varies directly as the cube of its radius.the diameter of a sphere made of lead is 14cm.prove by method of variationthat by melting the sphere 8 sphere can be formed each of diameter 7cm(suppose that after melting the volume cnstnt?

1 Answer
Jan 4, 2018

See the explanation below

Explanation:

The volume of a sphere is #v=4/3pir^3# where #r="the radius"#

#2xx"the radius"="diameter"#

Volume of the sphere of #"diameter"=14cm# is

#V=4/3pir^3=4/3pi(14/2)^3=4/3pi7^3#

Volume of a sphere of #"diameter"=7cm# is

#V_1=4/3pi(7/2)^3=4/3pi7^3/2^3=1/8(4/3pi7^3)#

So,

#8V_1=8*1/8(4/3pi7^3)=V#