If the radius of the base of a right circular cylinder is decreased by 27% and its height is increased by 165%, then what is the percentage increase (closest integer) in its volume?​

Correct option is C

Given:

Radius of the cylinder is decreased by 27%

Height of the cylinder is increased by 165%

Find the percentage increase (closest integer) in volume.

Concept Used:

Volume of a right circular cylinder depends on the square of radius and height.

Formula Used:

Volume of cylinder = $$\pi r^2 h$$​​

If r changes by x% and h by y%:

New Volume Factor = $$\left(1+\frac{x}{100}\right)^2 \left(1+\frac{y}{100}\right)$$​​

Solution:

Decrease in radius by 27%: r ➔ 0.73r

Increase in height by 165%: h ➔ 2.65h

New volume:

V' = $$\pi (0.73r)^2 (2.65h)$$​​

​$$\frac{V'}{V} = (0.73)^2 \times 2.65 \\ \ \\= 0.5329 \times 2.65 \approx 1.412$$​​

Percentage change in volume:

(1.412 - 1) × 100 = 41.2% = 41%(approx.)

Alternate Solution(Exam-hall trick):