Final answer:
To determine the appropriate percentage change in the volume and curved surface area of a cylindrical tunnel after a 4% reduction in radius and 2% increase in height, the new volume is calculated to have decreased by 7.84% and the new curved surface area has decreased by 2.08%.
Step-by-step explanation:
To determine the percentage change in volume and curved surface area of the cylindrical tunnel, we need to calculate the new values after the radius is reduced by 4% and the height is increased by 2%.
Let's assume the original radius is r and the original height is h.
The new radius after a 4% reduction is r - 0.04r = 0.96r.
The new height after a 2% increase is h + 0.02h = 1.02h.
To calculate the new volume, we use the formula V = πr²h.
The new volume V' = π(0.96r)²(1.02h) = 0.9216πr²h.
Therefore, the percentage change in volume is (V' - V)/V * 100% = (0.9216πr²h - πr²h)/πr²h * 100% = -7.84%.
The curved surface area of a cylinder is calculated using the formula CSA = 2πrh.
The new curved surface area CSA' = 2π(0.96r)(1.02h) = 1.9584πrh.
Therefore, the percentage change in curved surface area is (CSA' - CSA)/CSA * 100% = (1.9584πrh - 2πrh)/2πrh * 100% = -2.08%.