Question
Area of a rectangle is equal to the total surface area
of a hemisphere having volume 3456 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 = 3456 r3 = 1728 r = 12 So, the total surface area of the hemisphere = 3 × π × 12² = 3 × 3 × 12² = 1296 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 = 1296 x² = 576 x = 24 So the breadth of the rectangle = 24 cm Length of the rectangle = 24 × 2.25 = 54 cm So the perimeter of the rectangle = 2 × (54 + 24) = 156 cm
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