Question
Area of a rectangle is equal to the total surface area
of a hemisphere having volume 9826 cm³ . Find the perimeter of the rectangle if its length is 125% more than its breath. (Take π = 3)Solution
Let, the radius of the hemisphere be ‘r’ cm. So according to question: 2/3 × 3 × r3 = 9826 r3 = 4913 r = 17 So, the total surface area of the hemisphere = 3 × π × 17² = 3 × 3 × 17² = 2601 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 = 2601 x² = 1156 x = 34 So the breadth of the rectangle = 34 cm Length of the rectangle = 34 × 2.25 = 76.5 cm So the perimeter of the rectangle = 2 × (76.5 + 34) = 221 cm
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