The radius of a cylinder is increased by 150 cm and its height is decreased by 20 cm. What is the percentage increase in its volume?

The volume of a cylinder is given by $$V = \pi r^{2}h$$ where $$r$$ is the radius and $$h$$ is the height.

1. 150 % increase in radius means the radius becomes
$$r_{\text{new}} = r + 1.5r = 2.5r$$

2. 20 % decrease in height means the height becomes
$$h_{\text{new}} = h - 0.2h = 0.8h$$

3. New volume:
$$V_{\text{new}} = \pi (r_{\text{new}})^{2}(h_{\text{new}})$$ $$= \pi (2.5r)^{2}(0.8h)$$ $$= \pi r^{2}h \times 2.5^{2} \times 0.8$$ $$= \pi r^{2}h \times 6.25 \times 0.8$$ $$= \pi r^{2}h \times 5$$ $$= 5V$$

4. Increase in volume:
$$V_{\text{new}} - V = 5V - V = 4V$$

5. Percentage increase:
$$\frac{4V}{V}\times 100 = 400\%$$

Hence, the volume of the cylinder increases by 400 %.
Option B which is: 400%