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: D
Explanation
Given:
Length of rectangle : Width = 14 : 11
Perimeter of rectangle = 150 cm
Radius of cylinder = 105% of height
By formula:
Perimeter = 2(l + b)
Area of rectangle = l × b
Top surface area of cylinder = πr²
Curved surface area of cylinder = 2πrh
Let
Length = 14x
Width = 11x
2(14x + 11x) = 150
2(25x) = 150
50x = 150
x = 3
Length = 42 cm
Width = 33 cm
Area of rectangle = 42 × 33 = 1386 cm²
Now
πr² = 1386
22/7 × r² = 1386
r² = 441
r = 21 cm
Radius = 105% × Height
21 = 1.05h
h = 20 cm
Curved surface area= 2πrh= 2 × 22/7 × 21 × 20= 2640 cm²