Question

A solid sphere of radius 15 cm is melted & recast into solid right circular cones of radius 20 cm and height 8 cm.Calculate the number of cones created

Answer 1

Let number of cones created are `x`.
Then, Volume of solid sphere = x*Volume of circular cones
`=>4/3piR^3 = x**1/3pir^2h=> 4R^3 = xr^2h`
Here, `R = 15cm, r = 20cm, h = 8cm`
So, putting these values,
`4**15**15**15 = x**20**20**8`
`=>x = (45**3)/(4**8) = 135/32 = 4.28`
As `x` is the number of circular cones, so it will be a whole number.
`:. x = 4`
So, `4` circular cones will be created.