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 .
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Find the area of the shaded region from figure , if the diameter of the circle with centre O is 28cm and AQ = 1/4AB
Answers
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
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area of the shaded portion = 3758.86 m²
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