Question

the curved surface area of a cylinder is 1320 cm square and it's base has a diameter 14 cm. Find the height and the volume of the cylinder

Answer 1

Given:

• The curved surface area(CSA) of a cylinder is 1320 cm square
• The base diameter of the cylinder is 14 cm

To be found:

The hight and the volume of the cylinder.

Given,

Diameter = 14

And we know that

∴ 2Radius = diameter

⇒ Radius = diameter ÷ 2

⇒ Radius = 14 ÷ 2

⇒ Radius = 7 cm

∴ So Radius (r) = 7 cm

$\star$ The formula to find the Curved Surface Area(CSA) of cylinder

= 2πrh unit sq.

So,

⇒ 2πrh = 1320

⇒ $2 \times \frac{22}{\not7} \times \not7 \times h = 1320$

⇒ $44h = 1320$

⇒ $h = 1320 \div 44$

⇒ $h = 30 cm$

∴ So the height of the cylinder is 30 cm.

Now,

The volume of the cylinder,

= πr²h unit sq.

$=\frac{22}{7} \times (7)^{2} \times 30$

$=\frac{22}{\not7} \times (\not7) \times (7) \times 30$

$= 22 \times (7) \times 30$

= 4620 cm cube

Hence,

The height of the cylinder is 30cm

And the volume of the cylinder is 4620 cm cube.

Answer 2

Given ,

CSA of cylinder = 1320 cm²

Diameter (d) = 14 cm

So , radius (r) = 14/2 = 7 cm

$\boxed{ \tt{CSA = 2\pi rh}}$

Thus ,

$\tt \implies 1320 = 2 \times \frac{22}{7} \times 7 \times h$

$\tt \implies1320 = 44 \times h$

$\tt \implies h = \frac{1320}{44}$

$\tt \implies h = 30 \: \: cm$

Hence , the height of cylinder is 30 cm

Now , the volume of cylinder is given by

$\boxed{ \tt{Volume = \pi {(r)}^{2} h}}$

Thus ,

$\tt \implies Volume = \frac{22}{7} \times 7 \times 7 \times 30$

$\tt \implies Volume = 154 \times 30$

$\tt \implies Volume = 4620 \: \: {cm}^{3}$

Hence , the volume of cylinder is 4620 cm³