Question

if cylinders radius is increased by 50% and height is decreased by 50% how much percent its volume changes​

Answer 1

Answer:

12.5% increased

Explanation:

Question says that,

If the radius is increased by 50% and height is reduced by 50%. Find the change in volume (in %)

We know that,

→ Volume of a cylinder = $\boldsymbol{ \pi r^2h}$

Where,

• ‘r' denotes the radius.
• ‘h’ is the height.

Now,

$\boldsymbol r$ is increased by 50%

$= r + (50\% \: { \rm of } \: r)$

$= r + \dfrac{r}{2}$

$= \dfrac{3r}{2}$

Also, $\boldsymbol h$ is decreased by 50%

$= h - (50 \% \: { \rm of } \: h)$

$= \dfrac{h}{2}$

New volume of the cylinder:-

$= \pi \times \bigg( { \dfrac{3r}{2} \bigg)}^{2} \times \bigg( \dfrac{h}{2} \bigg)$

$= \dfrac{9\pi {r}^{2}h }{8}$

Since,

New volume > Original volume

Hence, there's a increase in volume.

Volume increased:-

$= \dfrac{9\pi {r}^{2} h}{8} - \dfrac{\pi {r}^{2} h}{1}$

$= \dfrac{9\pi {r}^{2} h - 8\pi {r}^{2}h }{8}$

$= \dfrac{\pi {r}^{2} h}{8}$

Increase in % is given by,

$= \rm \dfrac{increase \: in \: volume}{original \: volume} \times 100$

$= \dfrac{\pi {r}^{2}h }{8 \times \pi {r}^{2}h } \times 100$

$= 12.5\%$

${ \textsf{ \textbf{Hence, the increase in volume is \green{12.5\%}}}}$

__________________________

Answer 2

PROVIDED INFORMATION :-

if cylinders radius is increased by 50% and height is decreased by 50%

QUESTION :-

if cylinders radius is increased by 50% and height is decreased by 50% how much percent its volume changes

To Find :-

how much percent its volume changes = ?

SOLUTION :-

Let Radius of cylinder = R

Its height = H

Its volume, V₁ = π R² H

Volume of new cyliner, V₂ = π (R-0.5 R)²

(H+0 . 5H)

V₂ = π (0.5R)² (01. 5H)

= π × 0.25 R² × 0 1 . 5 H = 0.375 π R² H

V₂ = π ( 0. 5 R)² ( 0 1 . 5 H )

= π × 0.25 R² × 01. 5H = 0.375 π R² H

V₂= 37.5% of V₁

Hence, the volume is decreased

by 62.5%