Question : A solid cylinder having a radius of base of 28 cm and a height of 24 cm is bisected from its height to get two identical cylinders. What will be the percentage increase in the total surface area?
Option 1: 61.72%
Option 2: 41.92%
Option 3: 53.85%
Option 4: 48.64%
Correct Answer: 53.85%
Solution :
Given,
Radius = 28 cm and Height = 24 cm
Let the radius and height of the cylinder be $r$ and $h$ respectively.
⇒ Radius and height of smaller cylinder are $r$ and $\frac{h}{2}$
The surface area of the old cylinder = $2πr^2 + 2πrh = 2πr(r + h)$
And The combined surface area of 2 small cylinder $= 2(2πr(r + \frac{h}{2}))
⇒ 2πr(2r + h)$
⇒ Increase in area $= 2πr(2r + h) – 2πr(r + h) = 2πr(r) = 2πr2$
So, the required percentage increase
= $100 × \frac{2\pi r^2}{2πr(r + h)}$
= $100 × \frac{r}{r+h}$
= $100 × \frac{28}{28+24}$
= $100 × \frac{28}{52}$
= $53.85$%
Hence, the correct answer is 53.85%.
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