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The diameters of the internal and external surfaces of a hollow hemispherical shell are 6cm and 10cm respectively. If it is melted and recast into a solid cylinder of diameter 14cm , find the height of the cylinder .========================================================Find the area of the shaded region from figure , if the diameter of the circle with centre O is 28cm and AQ = 1/4AB |
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Answer» Given : The diameters of the internal and external surfaces of a hollow hemispherical shell are 6cm and 10cm . melted and RECAST into a solid cylinder of diameter 14cm To find : Height of cylinder Solution: internal and external Diameter = 6cm & 10 cm => internal & external RADIUS = 3cm & 5 cm Volume of hemisphere = (2/3)π(5³ - 3³) = 196π/3 cm³ Volume of solid cylinder = πr²h diameter = 14 => radius = 7 cm h = height in cm = π(7)²h = 49πh cm³ 49πh = 196π/3 => h = 4/3 cm = 1.33 cm AB = Diameter = 28 cm AQ = (1/4) AB = (1/4) 28 = 7 cm => radius = (7/2) cm => BQ = 28 - 7 = 21 cm => Radius = (21/2) cm Area of shaded REGION = (1/2)π (7/2)² + (1/2)π (21/2)² = (1/8) (22/7) * 7² + (1/8) (22/7) *21² = 154/8 + 1386/8 =1540/8 = 192.5 cm² Learn more: a cuboid shaped slab of iron whose dimensions are 55 cm by 40 cm ... A solid cube made of steel is melted and recast such that its length ... area of the shaded portion = 3758.86 m² |
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