The curved surface area of a cylinder is 2268 cm². The difference between the radius and the slant height of a cone is 32 cm, and its curved surface area measures 6435 cm². What is the radius of the cylinder in ______ cm, and what is the difference in volume between the cone and the cylinder in _______ cm³? [Taken ᴨ = 3] Which of the following options correctly fill in the blanks in the same order as given?
I. 27, 30356
II. 45, 9954
III. 52, 2016

ATQ, Radius of Cone = r cm Slant Height of Cone = (r + 32) cm 3 × r × (r + 32) = 6435 r² + 32r = 2145 r² + 32r - 2145 = 0 (r + 65)(r - 33) = 0 r = 33 cm l = 33 + 32 = 65 cm Height of Cone = √(65²- 33²) = √(4225 - 1089) = √3136 = 56 cm Volume of Cone = 1/3 × 3 × 33² × 56 = 60984 cm³ Option I, Radius of Cylinder = 27 cm Height of Cylinder = 2268/(2 × 3 × 27) = 14 cm Volume of Cylinder = 3 × 27² × 14 = 30618 cm³ Difference = 60984 - 30618 = 30366 cm³ (False) Option II, Radius of Cylinder = 45 cm Height of Cylinder = 2268/(2 × 3 × 45) = 8.4 cm Volume of Cylinder = 3 × 45² × 8.4 = 51030 cm³ Difference = 60984 - 51030 = 9954 cm³ (True) Option III, Radius of Cylinder = 52 cm Height of Cylinder = 2268/(2 × 3 × 52) = 189/26 cm Volume of Cylinder = 3 × 52² × 189/26 = 58968 cm³ Difference = 60984 - 58968 = 2016 cm³ (True) Hence, Only II and III is true.