Question : A solid cylinder having a radius of the base of 7 cm and a length of 20 cm is directed from its height to get two identical cylinders. What will be the percentage increase in the total surface area?
Option 1: 29.78
Option 2: 25.93
Option 3: 27.62
Option 4: 32.83
Correct Answer: 25.93
Solution :
Given: radius of original cylinder = 7 cm
Height of cylinder = 20 cm
Let radius and height of smaller cylinder be $r$ and $\frac{h}{2}$
Surface Area of old cylinder = $2\pi r^2 + 2\pi rh = 2\pi r(r + h)$
Combined Surface area of 2 small cylinders = $2(2\pi r(r + \frac{h}{2})) = 2\pi r(2r + h)$
Difference in the two surface areas = $2\pi r^2$
Percentage increase
= $ 100 \times \left(\frac{2\pi r^2}{2\pi r(r + h)}\right)$
= $100 \times \left(\frac{r}{r + h}\right)$
= $100 \times \left(\frac{7}{7 + 20}\right)$
= $100 \times \frac{7}{27}$
$ \approx 25.93$
Hence, the correct answer is 25.93.
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