Question : A solid cylinder having a radius of base of 21 cm and a height of 16 cm is bisected from its height to get two identical cylinders. What will be the percentage increase in the total surface area?
Option 1: 56.76%
Option 2: 42.52%
Option 3: 62.34%
Option 4: 48.88%
Correct Answer: 56.76%
Solution :
Given: the cylinder's base radius = 21 cm and height = 16 cm
Let the base radius and height of the original cylinder be $r$ and $h$ respectively.
⇒ The base radius and height of the smaller cylinder are $r$ and $\frac{h}{2}$ respectively.
Now, the surface area of the original cylinder = $2\pi r(r+h)$
and the surface area of the smaller cylinders = $2×2\pi r(r+\frac{h}{2})$ = $2\pi r(2r+h)$
So, the increase in area = $2\pi r(2r+h)-2\pi r(r+h)$ = $2\pi r^2$
Thus, increase percentage = $\frac{\text{increased area}}{\text{original area}}×100$
= $\frac{2\pi r^2}{2\pi r(r+h)}×100$
= $\frac{r}{r+h}×100$
= $\frac{21}{21+16}×100$
= $\frac{21}{37}×100$
$\approx$ 56.76%
Hence, the correct answer is 56.76%.
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