Question : The ratio between the height and radius of the base of a cylinder is 7 : 5. If its volume is 14836.5 cm3, then find its total surface area (take $\pi$ = 3.14).
Option 1: 3391.2 cm2
Option 2: 5391.2 cm2
Option 3: 4391.2 cm2
Option 4: 5591.2 cm2
Correct Answer: 3391.2 cm 2
Solution : Given, The ratio between the height and radius of the base of a cylinder is 7 : 5. Volume is 14836.5 cm 3 Let the height be $7x$ and the radius be $5x$. According to the question, Volume of cylinder = $\pi r^2h$ ⇒ $14836.5 = \pi (5x)^2 × 7x$ ⇒ $14836.5 = (3.14)(25x^2) × 7x$ ⇒ $175x^3= \frac{14836.5}{3.14}$ ⇒ $x^3 = \frac{4725}{175}$ ⇒ $x^3 = 27$ $\therefore x = 3$ So, the radius $= 5x = 5 × 3 = 15$ cm and the height $= 7x = 7 × 3 = 21$ cm Now, the total surface area of the cylinder = $2\pi r(r + h)$ = 2 × (3.14) × 15 × (15 + 21) = 3391.2 cm 2 Hence, the correct answer is 3391.2 cm 2 .
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