Question

A toy is in the form of a cone mounted on a hemisphere. The diameter of the base of the cone and
that of hemisphere is 18 cm and the height of cone is 12 cm. Calculate the surface area of the
toy. (Take 'IT=3.14).

Answer 1

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Answer 2

Given:

A toy formed by mounting a cone on a hemisphere.

Diameter of the cone and hemisphere = 18 cm

Height of the cone = 12 cm

To Find:

Surface area of the toy

Solution:

Since the diameter of the cone and the hemisphere = 18 cm

          the radius of the cone and the hemisphere (r) = 18/2 = 9 cm

Height of cone (h) = 12 cm

Slant height to cone (l) = $\sqrt{h^{2}+r^{2} }$

Therefore,

l = $\sqrt{12^{2} +9^{2} }$ cm

l = 15 cm

Curved surface area of cone = πrl

                                                 = (3.14)(9)(15)

                                                 = 3.14 * 135 cm²

Curved surface area of hemisphere = 2πr²

                                                            = 2(3.14)9²

                                                            = 3.14 * 162 cm²

total surface area of toy = CSA of cone + CSA of hemisphere

                                        = 3.14*135 + 3.14*162

                                        = 3.14 (297)

                                        = 932.58 cm²

Hence the surface area of the toy is 932.58 cm²