Question
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, 2016Solution
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.
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