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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 the cone are 6 cm and 4 cm, respectively. Determine the surface area of the toy.



Answer -


Given that,

The height of the cone(h) = 4 cm

Diameter of the cone(d) = 6 cm

So, its radius (r) = 3

Let, ‘l’ be the slantheight of cone.

Then, we know that

l2 = r2 +h2

l2 = 32 +42 = 9 + 16 = 25

l = 5 cm

Hence, the slantheight of the cone (l) = 5 cm

So, the curved surfacearea of the cone (S1) = πrl

S1 = π(3)(5)

S1 =47.1 cm2

And, the curvedsurface area of the hemisphere (S2) = 2πr2

S2 = 2π(3)2

S2 =56.23 cm2

So, the total surfacearea (S) = S+ S2

S = 47.1 + 56.23

S = 103.62 cm2

Therefore, the curvedsurface area of the toy is 103.62 cm2

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