If the radius of the base of a right circular cylinder is decreased by 27% and its height is increased by 237%, then what is the percentage increase (closest integer) in volume?

Correct option is A

Given:

Radius decreased by 27% 

Height increased by 237% 

Formula Used:

Volume of cylinder V = $$\pi r^2 h$$​​

Percentage increase = $$\left[\frac{\text{New volume}} { \text{Original volume}} - 1\right] \times 100\%$$​​

Solution:

New radius = $$r \times (1 - 0.27)$$​ = 0.73r

New height = $$h \times (1 + 2.37)$$​= 3.37h

​$$V_{\text{new}} = \pi (0.73r)^2 \times 3.37h \\ \ \\ = \pi r^2 h \times (0.73^2 \times 3.37)$$

​​$$=\pi r^2h( 1.7957)$$​​

Percentage increase:

​$$= (1.7957 - 1) \times 100 = 79.57\% \approx 80\%$$

Alternate Solution:

​$$\Delta = x + y + z + \frac{xy}{100} + \frac{yz}{100} + \frac{xz}{100} + \frac{xyz}{10000}$$​​

​$$x = -27, \quad y = -27, \quad z = 237$$​​

Now, 

​$$= (-27) + (-27) + 237 + \frac{(-27)(-27)}{100} + \frac{(-27)(237)}{100} + \frac{(-27)(237)}{100} + \frac{(-27)(-27)(237)}{10000}\\ \ \\ = 183 +7.29-63.99-63.99 +17.2359 \\ \ \\ = 79.5459 \approx 80\%$$​​