The radius of the cylinder is increased by 50%, and its height is decreased by 40%. We need to calculate the percentage change in its volume.

Given:
Radius increased by 50% = original radius + 50% of original radius
Height decreased by 40% = original height - 40% of original height

Formula for the volume of a cylinder:
V = πr²h

Step 1: Find the original volume of the cylinder:
Let's assume the original radius of the cylinder is 'r' and the original height is 'h'.
Original volume (V1) = πr²h

Step 2: Calculate the new radius and height:
Since the radius is increased by 50%, the new radius (r2) will be:
r2 = r + 50% of r
= r + (50/100) * r
= r + 0.5r
= 1.5r

Since the height is decreased by 40%, the new height (h2) will be:
h2 = h - 40% of h
= h - (40/100) * h
= h - 0.4h
= 0.6h

Step 3: Find the new volume of the cylinder:
New volume (V2) = π(1.5r)²(0.6h)
= π(2.25r²)(0.6h)
= 1.35πr²h

Step 4: Calculate the percentage change in volume:
Percentage change in volume = ((V2 - V1) / V1) * 100
= ((1.35πr²h - πr²h) / πr²h) * 100
= (0.35πr²h / πr²h) * 100
= 0.35 * 100
= 35%

Therefore, the percentage change in volume is 35%.

Explanation:
When the radius of the cylinder is increased by 50%, the new volume increases by 35%. This is because the volume of a cylinder is directly proportional to the square of the radius. So, when the radius increases, the volume increases exponentially.

On the other hand, when the height of the cylinder is decreased by 40%, the new volume decreases by 40%. This is because the volume of a cylinder is directly proportional to the height. So, when the height decreases, the volume also decreases linearly.

Therefore, the overall percentage change in volume is the sum of the individual percentage changes. In this case, the increase in volume due to the increased radius outweighs the decrease in volume due to the decreased height, resulting in a net increase of 35%.

3.1%