Question

the curved surface area of the cylinder is 1760cm square and its volume is 12320cm cube .find its height

Answer 1

$\bf{\huge{\underline{\boxed{\rm{\red{Answer:}}}}}}$

Given :-

• Curved surface area of the cylinder = 1760 square cm
• Volume of the cylinder = 12320 cubic cm.

To find :-

• Height of the cylinder.

Solution :-

Let's first calculate the radius of the cylinder with surface area of 1760 cm²

We know that the surface area of cylinder is given by the formula,

$\bf{\large{\underline{\boxed{\rm{\blue{Surface\:area\:of\:cylinder\:=\:2(\pi\:r\:h\:)}}}}}}$

Plug in the values,

1760 = 2 π r h

Transport the 2 from the formula of the surface area of cylinder to the LHS make the surface area half it's initial value.

$\bf\large\frac{1760}{2}$ = π r h

880 = π r h -----> 1

Now, let's see if we can do something via using the formula for volume of the cylinder. Here's the formula,

$\bf{\large{\underline{\boxed{\rm{\green{Volume\:of\:cylinder\:= \pi\:r^2\:h}}}}}}$

Plug the given values. But before that we will do something more with the formula which will make our calculation quite a lot simple.

12320 = $\bf\large{\pi rh\:\times\:r}$

So as you can see πrh above, we can replace it with the value from equation 1,

12320 = 880 × r

$\bf\large\frac{12320}{880}$ = r

$\bf\large\frac{1232}{88}$ = r

Dividing by 11,

$\bf\large\frac{112}{8}$ = r

Dividing by 2,

$\bf\large\frac{56}{4}$ = r

Dividing by 2 again,

$\bf\large\frac{28}{2}$ = r

Dividing for last time,

14 = r

•°• Radius of the cylinder = 14 cm

Now just substutite this value of radius in the formula for volume of the cylinder, where π = 22/7

12320 = $\bf\large\frac{22}{7}$ × 14² × h

$\bf\large\frac{12320\times\:7}{22}$ = 196 × h

$\bf\large\frac{86240}{22}$ = 196h

3920 = 196h

$\bf\large\frac{3920}{196}$ = h

20 = h

•°• Height of the cylinder = 20 cm

$\bf{\huge{\underline{\boxed{\rm{\pink{Verification:}}}}}}$

For surface area of cylinder :-

• Surface area = 1760 cm²
• Radius = 14 cm
• Height = 20 cm
• π = 22/7

Plug in the values in the formula for surface area of cylinder.

1760 = 2 × $\bf\large\frac{22}{7}$ × 14 × 20

1760 = $\bf\large\frac{44}{7}$ × 280

1760 = $\bf\large\frac{12320}{7}$

1760 = 1760

LHS = RHS.

For volume of the cylinder :-

• Volume = 12320 cm³
• Radius = 14 cm
• Height = 20 cm
• π = 22/7

Plug in the given values in the formula for volume of the cylinder.

12320 = $\bf\large\frac{22}{7}$ × 14² × 20

12320 = $\bf\large\frac{22}{7}$ × 14 × 14 × 20

12320 = $\bf\large\frac{22}{7}$ × 196 × 20

12320 = $\bf\large\frac{22}{7}$ × 3920

12320 = $\bf\large\frac{86240}{7}$

12320 = 12320

LHS = RHS.

Hence our answer is right.