The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Prove that its height and radius are equal.

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Solution

$Let S_{1} and S_{2} be the curved surface area and total surface area of the circular cylinder, respectively . Then, S_{1} = 2 π r h, S_{2} = 2 π r (r + h) According to the question : S_{1} : S_{2} = 1 : 2 2 π r h : 2 π r (r + h) = 1 : 2 h : (r + h) = 1 : 2 \frac{h}{r + h} = \frac{1}{2} 2 h = r + h h = r Therefore, the height and the radiu s are equal.$

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The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Prove that its height and radius are equal.

Let S1 and S2 be the curved surface area and total surface area of the circular cylinder, respectively.Then, S1=2πrh , S2=2πrr+hAccording to the question: S1:S2=1:22πrh : 2πrr+h =1 : 2 h : r+h = 1 : 2 hr+h=12 2h=r+h h=rTherefore, the height and the radius are equal.