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Question
A toy is in the form of a cone surmounted on a hemisphere. The diameter of the base and the height of cone are 6cm and 4cm. determine surface area of toy?
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Solution
Given height of cone (h) = 4cm
Diameter of cone (d) = 6cm
∴Radius (r) =`6/2 =3 cm`
Let ‘l’ be slant height of cone
`l=sqrt(r^2+h^2)`
`=sqrt(3^2+4^2) =5cm`
l = 5cm
∴ Slant height of cone (l) = 5cm.
Curved surface area of cone (S1) = πrl
S1 = π(3)(5) = 47.1cm2
Curved surface area of hemisphere (S2) = 2πr2
`S_2=2pi(3)^2=56.52cm^2`
∴Total surface area(S) = S1 + S2
= 47.1 + 56.52
= 103.62cm2
∴ Curved surface area of toy = 103.62cm2
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