Question

if the radius of right circular cylinder is increased by 10% and height is decrease by 10% then what is the percentage change in volume of the cylinder due to this.​

Answer 1

Step-by-step explanation:

Let volume initial volume V , height h and radius r .

New volume

$V = \pi( r \times \frac{110}{100} ) {}^{2} \times (h \times \frac{90}{100} ) \\ \: \: \: \: = \pi {r}^{2} h( \frac{1089}{1000} )$

So percent change

$\% = \frac{89}{1000} \times 100 = 8.9\%$

Answer 2

Given : The radius of right circular cylinder is increased by 10% and height is decreased by 10%

To find : Percentage change in volume.

Solution :

We can simply solve this mathematical problem by using the following mathematical process. (our goal is to calculate the percentage change in the volume)

Let, the radius of the cylinder = r

and, the height of the cylinder = h

So, the volume of the cylinder :

= π × (radius)² × height

= πr²h

After increasing the radius becomes :

= r + (r × 10%)

= r + [r × (10/100)]

= r + (r/10)

= (10r + r)/10

= 11r/10

After decreasing the height becomes :

= h - (h × 10%)

= h - [h × (10/100)]

= h - (h/10)

= (10h - h)/10

= 9h/10

The new volume will be :

= π × (11r/10) × (9h/10)

= (1089πr²h/1000)

Now, new volume > initial volume

So,

The increase in the volume :

= New volume - Initial volume

= (1089πr²h/1000) - πr²h

= (1089πr²h - 1000πr²h)/1000

= (89πr²h/1000)

Percentage increase in the volume :

= 100 × (Increase in volume / Initial volume)

= 100 × [(89πr²h/1000) ÷ πr²h]

= 100 × [(89πr²h/1000) × (1/πr²h)]

= 8.9%

Hence, the volume increased by 8.9%