If the radius ofa right circular cylinder is decreased by 10%, and the heightis increased by 20%, then the percentage increase/decreasein its volumeis:

Volume of  right circular cylinder = $$\pi r^2h$$

Radius of a right circular cylinder is decreased by 10%, and the height is increased by 20% so,

r1 = r $$\times 90/100$$ = 0.9r

h1 = h $$\times 120/100$$ = 1.2h

Volume of new right circular cylinder =$$\pi r1^2h1$$ = $$\pi (0.9r)^2(1.2h)$$ = 0.972($$\pi r^2h$$)

Decrements  in volume =  $$\pi r^2h$$ - 0.972($$\pi r^2h$$) = 0.028($$\pi r^2h$$)

Percentage Decrements in volume = $$\frac{0.028(\pi r^2h)}{(\pi r^2h)} \times 100$$ = 2.8%