Question

State true or false:

The radius of a solid right circular cylinder decreases by $20\%$ and its height increases by $10\%$. Find the percentage change in its volume
Answer: Decrease 29.6%

• A. True
• B. False

Answer 1

The correct option is A True

volume of solid circular cylinder=
$V=\pi r^{2}h$
New solid circular cylinder=
radius is decreases by 20%, r(1-20/100)
radius =0.8r
and height is increases by 10%, h(1+20/100)=1.1h
volume of new solid circular cylinder=
$V^{\prime }=\pi {0.8r}^{2}1.1h$
$V^{\prime }=\pi \ast 0.704r^{2}h$
So, percentage change $=\frac{(V-V^{\prime })}{V}\ast 100$
$=(1-0.64\times 1.1)100$ = $29.6$ %