If the curved surface area of a solid cylinder is one-third of its total surface area, then what is the ratio ofits diameter to its height?
Curved surface area of a solid cylinder = $$\frac{1}{3} \times$$ total surface area
$$2\pi r h = \frac{1}{3} \times 2\pi r(r + h)$$
$$\frac{h}{r + h} = \frac{1}{3}$$
r = 3 - 1 = 2 units
h = 1 unit
Diameter = 2r = 2 $$\times$$ 2 = 4
Ratio of its diameter to its height = 4 : 1
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