If the radius of the base of a right circular cylinder is decreased by 30% and its height is increased by 224%, then what is the percentage increase (closest integer) in its volume?

Correct option is B

Given:

Radius decreased by 30% 

Height increased by 224%

Formula Used:

Volume of a cylinder = $$\pi r^2 h$$

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

Solution: 

New radius = 70% of original = 0.7r

 New height = 324% of original = 3.24h

Let initial volume ,V = $$\pi r^2 h$$​​

New volume = $$\pi (0.7r)^2 \times 3.24h$$​​

​$$= \pi r^2 h \times (0.49 \times 3.24)$$​​

​$$= \pi r^2 h \times 1.5876$$​​

Percentage change = $$(1.5876 - 1) \times 100 = 0.5876 \times 100 = 58.76\% \approx 59\%$$ 

Alternate Solution:

Net % change = $$x + y + z + \frac{xy}{100} + \frac{yz}{100} + \frac{xz}{100} + \frac{xyz}{100^2}$$​​

Substitute x = -30, y = -30, z = 224

​$$= -30 -30 + 224 + \frac{(-30) \cdot (-30)}{100} + \frac{(-30) \cdot 224}{100} + \frac{(-30) \cdot 224}{100} + \frac{(-30) \cdot (-30) \cdot 224}{10000}$$​​

​$$= 164 + 9 - 67.2 - 67.2 + 20.16\\ \ \\ = 58.76 \approx 59\%$$​​