Area of a rectangle is equal to the total surface area of a hemisphere having volume 13718 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 = 13718 r³ = 6859 r = 19 So, the total surface area of the hemisphere = 3 × π × 19² = 3 × 3 × 19² = 3249 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 = 3249 x² = 1444 x = 38 So the breadth of the rectangle = 38 cm Length of the rectangle = 38 × 2.25 = 85.5 cm So the perimeter of the rectangle = 2 × (85.5 + 38) = 247 cm