Question 14 - Case Study - CBSE Class 10 Sample Paper for 2022 Boards - Maths Basic [Term 2] - Solutions of Sample Papers for Class 10 Boards

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Krishnan agar is a small town in Nadia District of West Bengal. Krishnan agar 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 colors 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 Krishnan agar. 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 color 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.? 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 color 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: 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 Question 14 (i) (i) What is the ratio of the surface areas of red spherical apples in Doll-1 to that of spherical oranges in Doll-2.? Given that Ratio of diameters of red spherical apples in Doll-1 to that of spherical oranges in Doll-2 is 2:3 Thus, Ratio of Diameters of apples and oranges is 2 : 3 So, Ratio of radius of apples and oranges is 2 : 3 Let Radius of apples = 2x Radius of orange = 3x Since both are spherical Surface area of apple Surface area = 4𝜋(Radius of apple)2 = 4𝜋 × (2x)2 = 4𝜋 × 4x2 Surface area of orange Surface area = 4𝜋(Radius orange)2 = 4𝜋 × (3x)2 = 4𝜋 × 9x2 Thus, Ratio of surface areas = (𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑎𝑝𝑝𝑙𝑒)/(𝑆𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑜𝑟𝑔𝑎𝑛𝑔𝑒) = (4𝜋 × 4𝑥^2)/(4𝜋 × 9𝑥^2 ) = 𝟒/𝟗 Thus, required ratio is 4 : 9 Question 14 (ii) (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 Given that In Doll-3, male doll of blue color 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. Since Blue doll is melted to make a Cylindrical drum Volume of Doll = Volume of Drum Volume of Doll Volume of Doll = Volume of sphere + Volume of Cylinder = 𝟒/𝟑 𝝅𝒓^𝟑+𝝅𝒓^𝟐 𝒉 = 4/3 𝜋 × 3^3+𝜋 × 3^2 × 8 = 4𝜋 × 3^2+𝜋 × 9 × 8 = 36𝜋 +72𝜋 = 𝟏𝟎𝟖𝝅 Volume of Drum Drum is a cylinder of height h and radius 3 cm Volume of drum = 𝜋𝑟^2 ℎ = 𝜋 × 3^2 × ℎ = 𝟗𝝅𝒉 Now, Volume of Doll = Volume of Drum 𝟏𝟎𝟖𝝅=𝟗𝝅𝒉 108𝜋/9𝜋=ℎ 12=ℎ 𝒉=𝟏𝟐 𝒄𝒎 Thus, height of drum is 12 cm