Area of a rectangle is equal to the total surface area of a hemisphere having volume 1458 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 = 1458 r³ = 729 r = 9 So, the total surface area of the hemisphere = 3 × π × 9² = 3 × 3 × 9² = 729 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 = 729 x² = 324 x = 18 So the breadth of the rectangle = 18 cm Length of the rectangle = 18 × 2.25 = 40.5 cm So the perimeter of the rectangle = 2 × (40.5 + 18) = 117 cm