Subject
Quantitative Aptitude
Topic
Mensuration
A solid cylinder has a total surface area of 231 cm2. It its curved surface area is two thirds of the total surface area, the volume of the cylinder is
A solid cylinder has a total surface area of 231 cm2. It its curved surface area is two thirds of the total surface area, the volume of the cylinder is
ক)
269.5 cm2খ)
385 cm2গ)
308 cm2ঘ)
363.4 cm2ঙ)
364.4 cm2Explanation
We know that, Total surface area of a closed cylinder = area of curved surface + area of circular top and bottom ∴ Total surface area of closed cylinder = 2πrh + 2πr 2 = 2πr(r+h) sq. units Where, r = radius of base of cylinder, h = height of cylinder According to the condition given in the question, Curved surface area = (2/3) ×Total surface area ⇒ 3h = 2 × (r + h) ⇒ h = 2r Now, total surface area of a closed cylinder = 2πr(r+h) = 231 cm 2 ∴2πr(r+2r) = 231 6πr 2 = 231 ⇒ r = 7/2 = 3.5 cm ∴ Volume of a right circular cylinder = πr 2 h cubic units ⇒ Volume of the given cylinder = π r 2 × 2r = 2π r 3 ⇒ Volume of the given cylinder = π r 2 × 2r = 2π r 3 = 269.5 cm 3Related questions
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