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 5/6cm³. Find the height of the toy. Also, find the cost of painting the hemispherical part of the toy at the rate of ` 10 per cm².(Take π=22/7)
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Height of toy = 9.5 cm
Cost of painting the hemisphere = Rs. 770
Step-by-step explanation:
Radius of cone = radius of hemisphere = 3.5 cm
Total volume of toy = 166(5/6) cu.cm
Volume of cone = πr²h/3
Volume of hemisphere = 2π r³/3
Now πr²h/3 + 2πr³/3 = 166.83
πr²(h + 2r) = 500.5
(h + 7) = 500.5/(π3.5²)
h = 13 -7 = 6 cm
Height of toy = h + r = 6 + 3.5 = 9.5 cm
Surface area of hemisphere = 2πr² = 2 * 22/7 * 3.5 * 3.5 = 77 sq.cm.
Cost of painting the hemisphere = 10 * 77 = Rs. 770
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