A wooden toy is in the form of a cone surmounted on a hemisphere. The diameter of the base of the cone is 16 cm and its height is 15 cm. Find the cost of painting the toy at Rs. 7 per 100 cm².
Answers
Given : Radius of the hemisphere , r = 8 cm
Height of the cone, h = 15 cm
Slant height of the cone , l = √(h² + r²)
l = √(15² + 8²)
l = √(225 + 64)
l = √289
Slant height of the cone ,l = 17 cm
Total curved surface area of the toy = Curved surface area of hemisphere + Curved surface area of the cone
Total curved surface area of the toy = 2πr² + πrl
Total curved surface area of the toy = 2 × (22/7) × 8² + (22/7) × 8 × 17
= (44 × 64)/7 + (176 × 17)/7
= 2816/7 + 2992/7
= (2816 + 2992)/7
= 5808/7 cm²
Total curved surface area of the toy = 5808/7 cm²
Cost of painting the toy at ₹ 7 per 100 cm²
= 5808/7 × 7/100
= 5808/100
= ₹ 58.08
Hence, Cost of painting the toy is ₹ 58.08 .
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Answer:
Step-by-step explanation:
Slant height of the cone , l = √(h² + r²)
l = √(15² + 8²)
l = √(225 + 64)
l = √289
Slant height of the cone ,l = 17 cm
Total curved surface area of the toy = Curved surface area of hemisphere + Curved surface area of the cone
Total curved surface area of the toy = 2πr² + πrl
Total curved surface area of the toy = 2 × (22/7) × 8² + (22/7) × 8 × 17
= (44 × 64)/7 + (176 × 17)/7
= 2816/7 + 2992/7
= (2816 + 2992)/7
= 5808/7 cm²
Total curved surface area of the toy = 5808/7 cm²
Cost of painting the toy at ₹ 7 per 100 cm²
= 5808/7 × 7/100
= 5808/100
= ₹ 58.08