Question

the coverd surface area of cylinder of length 14 cm is 200 find the volume of cylinder

Answer 1

Answer:

Step-by-step explanation:

The curved surface area=200

The height=14cm

The CSA=2πrh

200 = 2×22/7×r×14

200 =44×r×2

200=88×r

200/88=r

10/11=r

The volume of cylinder= πr^2h

V=22/7{10/11}^2×14

V=22/7×10/11×10/11×14

V=2×10×10/11×2

V=20×20/11

V=400/11

V=36.3636364

Answer 2

Step-by-step explanation:

Given : The curved surface area of cylinder of length $14cm$  is $200cm$.

To find : The volume of cylinder.

Formula used : If a cylinder have radius 'r' , height 'h' then its,

Curved surface area $=2\pi rh$

Volume $=\pi r^2 h$

• Calculation for radius of cylinder 'r'

For calculating the volume of cylinder first we have to find the radius of cylinder 'r' so for radius we use curved surface formula and curved surface area is given to us,

Curved surface area $=200cm$     ,  $\pi = \frac{22}{7}$    and      $h=14cm$

Curved surface area of cylinder  $=2\pi rh$

                                               $2\pi rh=200$

                                  $2*\frac{22}{7} *r*14=200$

taking all terms of L.H.S except r to R.H.S,

                                                   $r=\frac{200*7}{2*22*14}$

                                                      $=\frac{25}{11}cm$

we get the radius of cylinder is $\frac{25}{11}cm$.

• Calculation for volume of cylinder

Now we have

$r=\frac{25}{11}cm$     ,      $\pi = \frac{22}{7}$    and      $h=14cm$

and the formula of volume is,

Volume of cylinder $=\pi r^2 h$

                                $= \frac{22}{7}*(\frac{25}{11})^2*14$

                                 $=\frac{22*14}{7} *\frac{(25)^2}{(11)^2}$

                                 $=44*\frac{625}{121}$

                                $=\frac{2500}{11} cm^3$

Hence we get the volume of cylinder is $\frac{2500}{11}cm^3$ .