Volume and Surface Area
4 solved SSC CGL Quantitative Aptitude previous year questions on Volume and Surface Area, each with the correct answer and a full explanation.
Q1
The curved surface area of a right cylinder is 3696 cm2. Its height is three times its radius. What is the capacity (in litres) of the cylinder? (Take π = )
✓ Correct answer: a) 25.872
ExplanationLet the radius of the cylinder be r, Then, height = 3r.Given: Curved surface area of cylinder = 3696 2πrh = 3696 ⇒ ⇒ ⇒r2 = 196 ⇒ r = 14 cm Therefore, height = 3 × 14 = 42 cm Now, volume of cylinder = πr2h = = 25872 cm3 We know that, 1000 cm3 = 1 litre Therefore, Capacity of the cylinder = = 25.872 litres
Q2
The height of a solid cylinder is 30 cm and the diameter of its base is 10 cm. Two identical conical holes each of radius 5 cm and height 12 cm are drilled out. What is the surface area (in cm2) of the remaining solid?
✓ Correct answer: a) 430π
ExplanationSlant height of (l) of cones = = = = 13 cm Surface area of the remaining solid = Curved surface area of cylinder + 2 × Curved surface area of cone that are drilled out on both sides = 2πr1h1 + 2πr2l = 2π × 5 × 30 + 2π × 5 × 13 = 300π + 130π = 430π cm2
Q3
The radii of two right circular cylinders are in the ratio 3 : 2 and the ratio of their volumes is 27 :16. What is the ratio of their heights?
✓ Correct answer: b) 3 : 4
ExplanationLet the radii of the cylinders be 3x and 2x and heights be h1 & h2 Now, ratio of volumes = Þ = Þ = Þ = Hence, ratio of heights is 3 : 4.
Q4
The area of the base of a right circular cone is 81π cm2 and its height is 12 cm. What is the curved surface area (in cm2) of the cone?
✓ Correct answer: b) 135 π
ExplanationArea of the base of a right circular cone = 81π cm2 ⇒ πr2 = 81π ⇒ r2 = 81 ⇒ r = 9 cm Slant height (l) = = = = = 15 cm Therefore, Curved surface area = πrl = π × 9 × 15 = 135π cm2
Practice more SSC CGL Quantitative Aptitude PYQs
Browse every Quantitative Aptitude chapter, or explore the full SSC CGL question bank.
🔢 All Quantitative Aptitude chapters →