Question

If the radius of a cylinder is decreased by 50 percent and the height increased by 50 percent then find percentage decreased in volume?

Answer 1

Answer:

62.5%

Step-by-step explanation:

Let r be the radius and h be the height of the cylinder.

∴ Original volume,V = πr²h

(i) Radius is increased by 50%:

New radius, r₁ = r - 50% of r

                       = r - (50/100) * r

                       = r - r/2

                       = r/2.

(ii) Height increased by 50%:

New height, h₁ = h + 50% of h

                        = h + (50/100) * h

                        = h + h/2

                        = 3h/2

∴ New volume,V₁ = πr₁²h₁

                             = π(r/2)²(3h/2)

                             = (3/8)πr²h

Decrease in volume = V - V₁

                                 = (1 - 3/8)πr²h

                                 = (5/8)πr²h

%Decrease in volume = [5/8πr²h/πr²h] * 100%

                                     = [5/8] * 100%

                                     = 62.5%.

Therefore, decrease in volume = 62.5%.

Hope it helps!

Answer 2

$\huge \bf{ \red{answer}}$

$\bf{62.5\%}$
$\bf{step \: by \: step \: explanation}$

$\sf{Given}$


The radius of a cylinder is decreased by 50 percent and the height increased by 50 percent.


so the

volume before reducing and increasing was

$\pi \: r^{2} h$

decrease in radius

=> r-50/100 r

=> r-1/2r

=> r-r/2

=> 2r-r/2

=> r/2

Now


increase in height

=> h+50/100h

=>h+1/2h


=> h+h/2

=> 2h+h/2

=> 3h/2

Now

new volume=

$\bf{\pi \: ( \frac{r}{2} )^{2} \frac{3h}{2} }$
$\pi \: \frac{ {r}^{2} }{4} \frac{3h}{2}$

$\pi \: \frac{3r ^{2} h}{8}$
$\pi \: \frac{3}{8} {r}^{2} h$


volume percent= orginal volume - new volume/original volume*100

=>
$\frac{\pi \: r ^{2} h - \frac{3}{8} \pi \: r ^{2}h }{\pi \: r ^{2}h } \times 100$

=>
$\frac{ \frac{8\pi \: r ^{2} h - 3\pi \: r ^{2}h }{8} }{\pi \: r ^{2} h} \times 100$


$\frac{ \frac{5\pi {r}^{2} h}{8} }{\pi {r}^{2} h} \times 100$


$\bf{ \frac{5}{8} \times 100}$

$\bf{ = > \: 62.5\%}$

$\huge{ \mathfrak{ \pink{ \: thanks}}}$