Area of a rectangle is equal to the total surface area of a hemisphere having volume 5488 cm³ . Find the perimeter of the rectangle if its length is 125% more than its breath. (Take π = 3)
Let, the radius of the hemisphere be ‘r’ cm. So according to question: 2/3 × 3 × r3 = 5488 r3 = 2744 r = 14 So, the total surface area of the hemisphere = 3 × π × 14² = 3 × 3 × 14² = 1764 cm² Let the breadth of the rectangle be ‘x’ cm So the length of the rectangle = 2.25x cm According to question: x × 2.25x = 1764 x² = 784 x = 28 So the breadth of the rectangle = 28 cm Length of the rectangle = 28 × 2.25 = 63 cm So the perimeter of the rectangle = 2 × (63 + 28) = 182 cm
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