Question : The radius and slant height of a cone are in the ratio 5 : 7. If its curved surface area is 1347.5 cm2, find its radius. $\mathrm{(Use ~\pi =\frac{22}{7})}$
Option 1: 15 cm
Option 2: 25.5 cm
Option 3: 17.5 cm
Option 4: 21 cm
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Correct Answer: 17.5 cm
Solution : Given, Radius : Slant height = 5 : 7 Let radius = 5$m$ and slant height = 7$m$ Curved surface area of the cone = 1347.5 cm 2 ⇒ $1347.5=\pi\times 5m\times 7m$ ⇒ $1347.5=\frac{22}{7}\times 35m^2$ ⇒ $m^2 = \frac{1347.5\times 7}{22\times 35}$ ⇒ $m^2 = \frac{9432.5}{770}=12.25$ ⇒ $m = \sqrt{12.25}=3.5$ So, the radius $= 5\times3.5 = 17.5$ cm Hence, the correct answer is 17.5 cm.
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