a solid wooden toy is in the form of a hemisphere surmounted b a cone of same radius. The radius of hemisphere is 3.5cm and the total wood used in 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
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volume of the toy = volume of hemisphere + volume of cone
= 2/3 x 22/7 x 3.5³ + 1/3 x 22/7 x 3.5² x h = 166 5/6
⇒ 89 5/6 + 12 5/6 h = 166 5/6
12 5/6 h = 166 5/6 - 89 5/6 = 77
h = 77 ÷ 12 5/6 = 6 cm
Height of toy = 6 + 3.5 = 9.5 cm
Surface area of hemispherical part = 2 x 22/7 x 3.5² = 77cm²
Cost of painting = 10 x 77 = Rs. 770
= 2/3 x 22/7 x 3.5³ + 1/3 x 22/7 x 3.5² x h = 166 5/6
⇒ 89 5/6 + 12 5/6 h = 166 5/6
12 5/6 h = 166 5/6 - 89 5/6 = 77
h = 77 ÷ 12 5/6 = 6 cm
Height of toy = 6 + 3.5 = 9.5 cm
Surface area of hemispherical part = 2 x 22/7 x 3.5² = 77cm²
Cost of painting = 10 x 77 = Rs. 770
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