A toy is in the form of a cone of radius 3.5cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm . Find the total surface area of the toy.
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Given :
Radius of the conical portion of the toy ,r = 3.5 cm
Total height of the toy , H = 15.5 cm
Height of the cone ,h = 15.5 – 3.5 = 12 cm
Slant height of the cone , l = √r² + h²
l = √3.5² + 12²
l = √12.25 + 144 = √156.25 = 12.5 cm
Slant height of the cone , l = 12.5 cm
Total surface area of the toy = Curved surface area of the cone + curved surface area of the hemisphere
TSA = πrl + 2πr²
TSA = πr(l + 2r)
= 22/7 × 3.5 ( 12.5 + 2 × 3.5)
= 22 × 0.5 ( 12.5 +7)
= 11 × 19.5
TSA = 214.5 cm²
Hence, the total surface area of the toy is = 214.5 cm²
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