If the radius of the base of a right circular cylinder is decreased by 20% and its height is increased by 134%, then what is the percentage increase (closest integer) in its volume?

Correct option is A

Given:

Radius decreased by 20%

Height increased by 134%

Formula Used:

Volume of Cylinder = πr²h

Percentage Change = $$\left( \frac{\text{New Volume} - \text{Original Volume}}{\text{Original Volume}} \right) \times 100$$​​

Solution:

New radius = 0.8r

New height = 2.34h

New Volume = $$\pi (0.8r)^2 \cdot 2.34h$$​​

​$$= \pi r^2 h \cdot 0.64 \cdot 2.34\\ \ \\ = \pi r^2 h(1.4976)$$ 

Thus, the ratio of the new volume to the original volume is:

​$$\frac{V'}{V} = \frac{\pi r^2 h(1.4976)}{\pi r^2 h}$$​​

​$$= 1.4976$$

​Percentage Increase = $$(1.4976 - 1) \times 100 = 49.76\%$$​​

Thus,  The volume increases by approximately 50%.

Alternate Solution: 

As from the volume of cylinder 

r = - 20%(decrease), h = +134%(increase) 

By successive formula; 

$$=-20-20+134 +\frac{(-20)(-20)}{100}+\frac{(-20)(134)}{100}+\frac{(-20)(134)}{100}++\frac{(-20)(-20)(134)}{10000}\\ \ \\ = 94 +4-26.8-26.8+5.36\\ \ \\ = 49.76\approx 50\%(increase)$$