Question
Area of a rectangle is equal to the total surface area
of a hemisphere having volume 8192 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 = 8192 r3 = 4096 r = 16 So, the total surface area of the hemisphere = 3 × π × 16² = 3 × 3 × 16² = 2304 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 = 2304 x² = 1024 x = 32 So the breadth of the rectangle = 32 cm Length of the rectangle = 32 × 2.25 = 72 cm So the perimeter of the rectangle = 2 × (72 + 32) = 208 cm
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