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
Solution
Correct Answer: Option A
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 + 2πr2 = 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
\(\therefore 2\pi rh\; = \frac{2}{3} \times 2\pi r\left( {r + h} \right)\)
⇒ 3h = 2 × (r + h)
⇒ h = 2r
Now, total surface area of a closed cylinder = 2πr(r+h) = 231 cm2
∴2πr(r+2r) = 231
6πr2 = 231
\(\Rightarrow {r^2} = \frac{{231}}{{6\pi }} = \;\frac{{49}}{4}\;c{m^2}\)
⇒ r = 7/2 = 3.5 cm
∴ Volume of a right circular cylinder = πr2h cubic units
⇒ Volume of the given cylinder = π r2 × 2r = 2π r3
⇒ Volume of the given cylinder = π r2 × 2r = 2π r3 = 269.5 cm3
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