Let h be the height of the cone and r be radius of its base
Now,
volume of the wooden toy = \(\frac{1}3πr^2h + \frac{2}3πr^3\)
= \(\frac{77}6(h + 7)\)
According to the question, \(\frac{77}6(h + 6)\) = 166\(\frac{5}6\)
⇒ h = 6 cm
The height of the wooden toy = 6 cm + 3.5 cm
= 9.5 cm
Now,
curved surface area of the hemispherical part = 2πr2
= 2π × (3.5)2
= 77 cm2
Hence
the cost of painting the hemispherical part of the toy at the rate of Rs.10 per cm2 = 77 × 10
= Rs.770