A solid wooden toy is in …

According to the question,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 $166 \frac { 5 } { 6 }$cm^3.
Given, radius of cone = radius of hemisphere = r
r = 3.5 cm.
Total volume, $V = 166 \frac { 5 } { 6 } \mathrm { cm } ^ { 3 } = \frac { 1001 } { 6 } \mathrm { cm } ^ { 3 }$ 
Let the height of cone be h.
Total volume = Volume of cone + Volume of hemisphere

$\frac { 1001 } { 6 } = \frac { 1 } { 3 } \pi r ^ { 2 } h + \frac { 2 } { 3 } \pi r ^ { 3 }$ 
or, $\frac { 1001 } { 6 } = \frac { 1 } { 3 } \pi ( 3.5 ) ^ { 2 } h + \frac { 2 } { 3 } \pi ( 3.5 ) ^ { 3 }$ 
or, $\frac { 1001 } { 6 } = \frac { 1 } { 3 } \pi [12.25 h + 2 \times 42.875 ]$ 
or, $\frac { 1001 \times 3 \times 7 } { 6 \times 22 } = 12.25 h + 85.75$ 
or, $\frac { 21021 } { 132 } = 12.25 h + 85.75$ 
or, $12.25 h = 159.25 - 85.75$ 
or, $h = \frac { 73.5 } { 12.25 } = 6$ 
Height of the toy = 6 + 3.5 = 9.5 cm.
Surface area of hemisphere $= 2 \pi r ^ { 2 }$ 
$= 2 \times \frac { 22 } { 7 } \times 3.5 \times 3.5$ 
$= 77 \mathrm { cm } ^ { 2 }$ 
Cost of painting $= 10 \times 77$ 
= Rs. 770