A toy is in the form of a cone mounted on a hemisphere such that the diameter of the base of the con...........

Quantitative Aptitude ( CCS) Mensuration 3D

A toy is in the form of a cone mounted on a hemisphere such that the diameter of the base of the cone is equal to that of the hemisphere. If the diameter of the base of the cone is 6 cm and its height is 4 cm, what is the surface area of the toy in sq cm ? (take π = 3.14)

93.62

103.62

113.62

115.50

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Explanation:

Given that, height of cone (h) = 4 cm
And, diameter of cone = diameter of hemisphere = 6 cm
? Base of cone is equal to that of hemisphere
∴ radius of cone = radius of hemisphere = r = 3 cm
Surface area of conical part = πrl
= 3.14 × 3 × √r² + h² (l =√r² + h² )
= 9.42 × √3² + 4²
= 9.42 × 5 = 47.1 cm²
Surface area of hemispherical part = 2πr²
= 2 × 3.14 × (3)² = 56.52 cm
∴ Surface area of the toy = 47.1 + 56.52 = 103.62 cm²