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Question
A solid wooden toy is in the form of a hemisphere surrounded 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` cm3. 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 cm2 .[Use`pi=22/7`]
Solution
Let h be the height of the cone and r be the radius of the base of cone.
The volume of the wooden toy = `1/3pir^2h+2/3pir^3`
`=1/3pir^2(h+2r)`
`=1/3xx22/7xx3.5xx3.5(h+7)`
`=77/6(h+7)`
According to the question,
`77/6(h+7)=166`
`=>77/6(h+7)=1001/6`
⇒h=6
The height of the wooden toy = 6 cm + 3.5 cm = 9.5 cm
Now,
Curved surface area of the hemispherical part = `2xx22/7xx3.5xx3.5 = 77 cm^2`
Hence, the cost of painting the hemispherical part of the toy = 77×10 = Rs 770
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