A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm, respectively. Determine the surface area of the toy. (Use π = 3.14)
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Answer:
The curved surface area of the toy is 103.62 cm² .
Step-by-step explanation:
Given :
Height of the cone (h) = 4cm
Diameter of the cone (d) = 6 cm
Radius of the cone & hemisphere , (r) = 3 [
Let, ‘l’ be the slant height of cone.
l = √r² + h²
l = √3² + 4² = √9 + 16 = √25
l = √25
l = 5 cm
Slant height of the cone (l) = 5 cm
Curved surface area of the cone (S1) = πrl
S1 = π(3)(5) = 15π cm²
S1 = 15π cm²
Curved surface area of the hemisphere (S2) = 2πr²
S2 = 2π(3)² = 2π × 9 = 18π cm²
S2 = 18π cm²
Total surface area of toy (S) = S1 + S2
S = 15π + 18π = π(15 + 18)
S = 3.14 × 33
[Given : π = 3.14 ]
S = 103.62 cm²
Hence, the curved surface area of the toy is 103.62 cm² .
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