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 its volume?

Given:

Initial radius of the cylinder = r.

Initial height of the cylinder = h.

Radius decreased by 27%, so new radius = 73% of r = 0.73r.

Height increased by 237%, so new height = 337% of h = 3.37h.

Formula Used:

Volume of a right circular cylinder = πr²h.

Calculation:

Initial Volume = πr²h.

New Volume = π(new radius)²(new height).

New Volume = π(0.73r)²(3.37h).

New Volume = π(0.73² × r²)(3.37h).

New Volume = π(0.5329 × r²)(3.37h).

New Volume = π(1.796873 × r²h).

Percentage Increase = [(New Volume - Initial Volume) / Initial Volume] × 100.

Percentage Increase = [(π(1.796873 × r²h) - πr²h) / (πr²h)] × 100.

Percentage Increase = [(1.796873 - 1) / 1] × 100.

Percentage Increase = 0.796873 × 100.

Percentage Increase ≈ 80%.

The percentage increase (closest integer) in the volume is approximately 80%.