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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