Q. 135.0( 5 Votes )
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.
Concept Used: Surface Area of Hemisphere = 2πr2
Curved Surface Area of cone = πrl
Lateral length of the cone = √(h2 + r2)
Where, r = radius of hemisphere and cone, and l = slant height of the cone.
The radius of the hemisphere = 8 cm
Height of the cone = 15 cm
Let us find the lateral length of cone first,
Lateral length of the cone = √(h2 + r2) = √(152 + 82) = 17 cm
The total curved surface area of the toy = 2πr2 + πrl
⇒ The total curved surface area of the toy
⇒ The total curved surface area of the toy = 829.714 cm2
Cost of painting the toy at Rs. 7 per 100 cm2 = Rs. 58.08
Hence, the cost of painting the toy is Rs. 58.08.
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