The length and breadth of a rectangle are in the ratio 14:11, respectively, and the perimeter of the rectangle is 150 cm. If the area of the rectangle is equal to the area of the top surface of a solid cylinder, then find the curved surface area of the cylinder given that its radius is 105% of its height.
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Correct answer: A
Explanation
Given:
Length of rectangle : Width = 14 : 11
Perimeter of rectangle = 150 cm
Area of upper surface of cylinder = Area of rectangle
Radius of cylinder = 105% of height
By formula:
Perimeter = 2(l + b)
Let l = 14x, b = 11x
2(14x + 11x) = 150
50x = 150
x = 3
Length = 14 × 3 = 42
Breadth = 11 × 3 = 33
Area of rectangle = l × b
Area of rectangle = 42 × 33 = 1386
Area of circle = πr²
πr² = 1386
r² = 1386 × 7 / 22 = 21
Radius = 105% × Height
21 = 1.05h
h = 20
Curved surface area of the cylinder = 2πrh
Curved surface area = 2 × 22/7 × 21 × 20 = 2640 cm²