Question

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?

Answer 1

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`