Previous Year Questions

From I:

Let the radius and height of the cylinder be 'R' and 'H' respectively.

Let the length and breadth of the rectangle be 'L' and 'B' respectively.

Curved surface area of cylinder = 2πRH = 4752 ----(i)

Area of the rectangle = LB = 3888 ----(ii)

And, Perimeter of the rectangle = 2(L + B) = 252 ----(iii)

From (iii) and (ii), we get

(L - B) = √[(L + B)² - 4LB] = √[126² - 4 * 3888] = √324 = 18

=> L - B = 18 ----(iv)

From (iii) and (iv), we get

L = 72 cm and B = 54 cm

Hence, R = 54/2 = 27 cm

Now, from (i), we get

2 * 22/7 * 27 * H = 4752

=> H = 4752 * 7/(2 * 22 * 27) = 28 cm

Thus, volume of the cylinder = πR²H = 22/7 * 27 * 27 * 28 = 64152 cm³

Hence, statement I alone is sufficient.

From II:

Let the side of a square be 'a' cm

Perimeter of the square = 4a = 56

Side = 14 cm.

Height = 14 cm.

Curved surface area of the cylinder = 2πRH = 1232 ----(i)

Radius = (1232 x 7)/(2 x 22 x 14)

Radius = 14 cm

Volume = 22/7 x 14² x 14 = 8624 cm³

Hence, statement II alone is sufficient.