Question : The height and the total surface area of a right circular cylinder are 4 cm and 8$\pi$ sq cm, respectively. The radius of the base of the cylinder is:
Option 1: $\left ( 2\sqrt{2}-2 \right )\ \text{cm}$
Option 2: $\left ( 2-\sqrt{2}\right )\ \text{cm}$
Option 3: $2\ \text{cm}$
Option 4: $\sqrt{2}\ \text{cm}$
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Correct Answer: $\left ( 2\sqrt{2}-2 \right )\ \text{cm}$
Solution :
Given: Height of the cylinder = 4 cm
Total surface area = 8$\pi$ cm
2
⇒ $2\pi r(h+r) = 8\pi$
⇒ $r(4+r) = 4$
⇒ $r^2+4r-4=0$
Using quadratic formula:
$r= \frac{-b\pm \sqrt{b^2-4ac}}{2a}$
⇒ $r= \frac{-4\pm \sqrt{4^2+4\times1\times4}}{2\times1}$
⇒ $r= \frac{-4\pm \sqrt{16+16}}{2}$
⇒ $r=\frac{-4\pm 4\sqrt{2}}{2}$
$\therefore r=(2\sqrt{2}-2)\ \text{cm}$
Hence, the correct answer is $(2\sqrt{2}-2)\ \text{cm}$.
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