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Mathematics

Find the ratio between the total surface area of a cylinder to its curved surface area given that its height and radius are 7.5 cm and 3.5 cm.

Mensuration

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Answer

We know,

Total surface area of cylinder = 2πr(h + r)

Curved surface area of cylinder = 2πrh

Total surface area of cylinderCurved surface area of cylinder=2πr(h+r)2πrh=(h+r)h=7.5+3.57.5=117.5=11075=2215.\dfrac{\text{Total surface area of cylinder}}{\text{Curved surface area of cylinder}} \\[1em] = \dfrac{2πr(h + r)}{2πrh} \\[1em] = \dfrac{(h + r)}{h} \\[1em] = \dfrac{7.5 + 3.5}{7.5} \\[1em] = \dfrac{11}{7.5} \\[1em] = \dfrac{110}{75} \\[1em] = \dfrac{22}{15}.

Hence, the ratio of total surface area of cylinder to curved surface = 22 : 15.

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