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The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2. If the total surface area is 616 cm2, what is the volume of the cylinder?
- a)539 cm3
- b)616 cm3
- c)1078 cm3
- d)1232 cm3
Correct answer is option 'C'. Can you explain this answer?
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The ratio of the curved surface area to the total surface area of a ri...
Suppose the radius and height of the cylinder is ‘r’ and ‘h’
Ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2
⇒ (2πrh) : (2πrh + 2πr2) = 1 : 2
⇒ h : (h + r) = 1 : 2
⇒ h = r
Since total surface area is 616 cm2
⇒ (2πrh + 2πr2) = 616
Putting h = r
⇒ 2π(r2 + r2) = 616
⇒ 4r2 = 196
⇒ r = 7 cm
⇒ h = r = 7 cm
∴ Volume of the cylinder = πr2h = (22/7) × 7 × 7 × 7 = 1078 cm3
⇒ (2πrh) : (2πrh + 2πr2) = 1 : 2
⇒ h : (h + r) = 1 : 2
⇒ h = r
Since total surface area is 616 cm2
⇒ (2πrh + 2πr2) = 616
Putting h = r
⇒ 2π(r2 + r2) = 616
⇒ 4r2 = 196
⇒ r = 7 cm
⇒ h = r = 7 cm
∴ Volume of the cylinder = πr2h = (22/7) × 7 × 7 × 7 = 1078 cm3
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The ratio of the curved surface area to the total surface area of a right circular cylinder is 1 : 2. If the total surface area is 616 cm2, what is the volume of the cylinder?a)539 cm3b)616 cm3c)1078 cm3d)1232 cm3Correct answer is option 'C'. Can you explain this answer?
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