Question

0.32
If the height of right circular cylinder is increased by
10% while the radius of base is decreased by 10% then
curved surface area of cylinder
(1) Remains same (2) Decreases by 1 %
(3) Increases by 1% (4) Increases by 0.1​

Answer 1

Answer:

pls see the above attachment..

Answer 2

Given:

The height of the right circular cylinder is increased by 10% while the radius of the base is decreased by 10%.

To find:

The percentage change in the curved surface area of the cylinder.

Solution:

As we know the curved surface area of a cylinder having radius 'r' and height 'h' is given by:

$= 2\pi \: r \: h$

Now,

proceeding to the solution,

Let the original radius of a right circular cylinder = r units

and

the original height of a cylinder = h units

So,

Its curved surface area is

$= 2\pi \: r \: h$

Now,

as given

The height of the right circular cylinder is increased by 10%,

So, the new height is

$= h + \frac{10}{100} h$

$= \frac{11h}{10}$

Also,

the radius of the base is decreased by 10%,

So, the new radius is

$= r - \frac{10}{100} r$

$= \frac{9r}{10}$

Hence,

the new curved surface area of a cylinder is

$= 2\pi \: \times \frac{9r}{10} \times \frac{11h}{10}$

$= 2\pi \: (\frac{99rh}{100} )$

Change in curved surface area

= new curved surface area of cylinder - the original curved surface area of the cylinder.

$= 2\pi \: (\frac{99rh}{100} ) - 2\pi \: r \: h$

$= 2\pi( \frac{99rh}{100} - rh)$

$= 2\pi \: (\frac{ - rh}{100} )$

(negative sign shows that there is a decrease in curved surface area of a right circular cylinder)

Now,

Percentage decrease in curved surface area of the cylinder

$= \frac{change \: in \: curved \: surface \: area}{original \: curved \: surface \: area} \times 100$

$= \frac{ 2\pi \: (\frac{ rh}{100} )}{2\pi \: r \: h} \times 100$

After solving we get,

$= 1\%$

Hence, the curved surface area of the cylinder (2) Decreases by 1 %.