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# A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy

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In the given problem toy is in the form of a cone so to find total surface area of toy we need to use cone surface area formula. This problem from RS Aggarwal Chapter Mensuration, Volume and Surface Area of Solid, Exercise 17A, Page number 787, problem number 13

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1. The radius of hemisphere as well as that of base of cone is r = 3.5 cm.

The height of toy = 15.5 cm.

The height of hemisphere, h = 3.5 cm and height of cone = 15.5 -3.5 = 12 cm.

Using Pythagoras Theorem,

slant height of cone is l = [√ (3. 5)² + (12)²]

= √[12. 25 +144]

= √156. 25

= 12. 5 cm.

Therefore, the Total surface area of toy = Curved surface of cone + Curved surface of hemisphere

= πrl +2πr²

= [22/7 * 3.5 *12.5] + [ 2 * 22/7 * 3.5²]

= 275 /2 + 77

= 275/2 +154

= 429/2

= 214. 5 cm²

∴ Total surface area of the toy is 214. 5 cm²

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