What will be the % decrease or increase in volume of a cylinder if its

1.	What will be the % decrease or increase in volume of a cylinder if its radius is decreased by 10% and height increased by 20%?1). 2.8% decrease2). 2.8% increase3). 3.2% increase4). 3.2% decrease
Answer» Volume of a cylinder = πr²h Given, its RADIUS is decreased by 10% and height increased by 20%. R = r – 10% of r = 0.9r H = h + 20% of h = 1.2h Volume of the new cylinder = πR²H ⇒ Volume of the new cylinder = π(0.9r)²× 1.2 h ⇒ Volume of the new cylinder = 0.972 πr²h Decrease in volume = πr²h – 0.972 πr²h = 0.028 πr²h % decreased in volume $(= \frac{{0.028{\rm{\pi }}{{\rm{r}}^2}{\rm{h}}}}{{{\rm{\pi }}{{\rm{r}}^2}{\rm{h}}}} \times 100\%= 2.8\%)$

What will be the % decrease or increase in volume of a cylinder if its radius is decreased by 10% and height increased by 20%?1). 2.8% decrease2). 2.8% increase3). 3.2% increase4). 3.2% decrease

Answer»

Volume of a cylinder = πr²h

Given, its RADIUS is decreased by 10% and height increased by 20%.

R = r – 10% of r = 0.9r

H = h + 20% of h = 1.2h

Volume of the new cylinder = πR²H

⇒ Volume of the new cylinder = π(0.9r)²× 1.2 h

⇒ Volume of the new cylinder = 0.972 πr²h

Decrease in volume = πr²h – 0.972 πr²h = 0.028 πr²h

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

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