Question
Area of a rectangle is equal to the total surface area
of a hemisphere having volume 4394 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 = 4394 r3 = 2197 r = 13 So, the total surface area of the hemisphere = 3 × π × 13² = 3 × 3 × 13² = 1521 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 = 1521 x² = 676 x = 26 So the breadth of the rectangle = 26 cm Length of the rectangle = 26 × 2.25 = 58.5 cm So the perimeter of the rectangle = 2 × (58.5 + 26) = 169 cm
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