The Question : Krishnanagar is a small town in Nadia District of West Bengal. Krishnanagar clay dolls are unique in their realism and quality of their finish. They are created by modelling coils of clay over a metal frame. The figures are painted in natural colours and their hair is made either by sheep’s wool or jute. Artisans make models starting from fruits, animals, God, goddess, farmer, fisherman, weavers to Donald Duck and present comic characters. These creations are displayed in different national and international museums.Here are a few images (not to scale) of some clay dolls of Krishnanagar.The ratio of diameters of red spherical apples in Doll-1 to that of spherical oranges in Doll-2 is 2:3. In Doll-3, male doll of blue colour has cylindrical body and a spherical head. The spherical head touches the cylindrical body. The radius of both the spherical head and the cylindrical body is 3cm and the height of the cylindrical body is 8cm. Based on the above information answer the following questions:(i) What is the ratio of the surface areas of red spherical apples in Doll-1 to that of spherical oranges in Doll-2.?(ii) The blue doll of Doll-3 is melted and its clay is used to make the cylindrical drum of Doll-4. If the radius of the drum is also 3cm, find the height of the drum.
Solution for the question :
(I) Let r1 and r2 be respectively the radii of apples and oranges
∵ 2r1: 2r2 = 2: 3
⇒ r1: r2 = 2: 3
4πr12: 4π22
2 = (r1/r2)2
= (2/3)2
= 4: 9
(ii) Let the height of the drum be h.
Volume of the drum = volume of the cylinder + volume of the sphere
π32h = (π32 × 8 + 4/3π33) cm3
⇒ h = (8 + 4)cm
⇒ h = 12vm
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