A solid wooden toy is in the form of a hemisphere surmounted by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is `166 5/6 cm^3`. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of Rs. 10 per `cm^2`

Explanation

Let the height of the conical part be h.
Radius of the hemisphere , r
= radius of the cone `=3.5 cm = 7/3 cm`
Volume of the wood used in making the toy
= volume of the hemisphere + volume of the cone `=2/3 pir^3+1/3pir^3h=1/3pir^2(2r +h)`
`=1/3xx 22/7xx7/2xx7/2xx(2 xx7/2+h)=77/6 (7+h)`
But the volume of the wood `= 166""5/6cm^3 =(1001)/(6)cm^3`
`therefore77/6(7+h)=(1001)/(6)rArr7+h =(1001)/(6)xx6/77=13`
`rArr =(13-7)cm=6 cm`
So the height of the toy `= h+r =(6+ 3.5)cm = 9.5 cm `
Area to be painted = curved surface area of the hemisphere
`=2pir^2=(2xx22/7xx7/2xx7/2)cm^3`
`=77cm^2`
Hence , cost of painting `=₹(77 xx 10 )= ₹ 770 `