Name: Volume of a Cylinder: Examples
Uploaded: 2019-07-19
Duration: 3 min 51 s
Description: Need to know how to find the volume of a cylinder? Well, you're in the right place! In this video, we look at how to find the volume of a cylinder through some examples.

Question

A hollow metal cylindrical disc is

3 cm

thick and its external diameter is

14 cm

. If its height is

5 cm

, find its volume and total surface area. [Use

π = 3.14

]

Accepted Answer

We know that the volume and the lateral surface area of a cylinder are given by $π r^{2} h$ and $2 π r h$ , where $r$ is the radius and $h$ is the height of the cylinder.

Also, the area of a circle is $π {(radius)}^{2}$ .

Let the outer and the inner radius of the cylinder be $R$ and $r$ , respectively.

So, $R = \frac{14}{2} = 7 cm$ [The radius is half the diameter]

And, $r = 7 - 3 = 4 cm$ [Given, the cylinder is $3 cm$ thick]

The height of the cylinder is $h = 5 cm$ .

The volume of the cylindrical disc $= {πR}^{2} h - {πr}^{2} h = πh (R^{2} - r^{2})$

$= 3.14 \times 5 \times (7^{2} - 4^{2}) = 15.7 \times (49 - 16) = 15.7 \times 33 = 518.1 {cm}^{3}$ .

The total surface area of the cylindrical disc $= 2 πRh + 2 πrh + 2 {πR}^{2} - 2 {πr}^{2}$

$= 2 π h (R + r) + 2 π (R^{2} - r^{2})$

$= 2 \times 3.14 \times 5 (7 + 4) + 2 \times 3.14 (7^{2} - 4^{2})$

$= 2 \times 3.14 \times 5 \times 11 + 2 \times 3.14 (49 - 16)$

$= 2 \times 3.14 \times 5 \times 11 + 2 \times 3.14 \times 33$

$= 345.4 + 207.24$

$= 552.64 {cm}^{2}$ .

Therefore, the volume and total surface area of the cylindrical disc are $518.1 {cm}^{3}$ and $552.64 {cm}^{2}$ , respectively.

A hollow metal cylindrical disc is $3 cm$ thick and its external diameter is $14 cm$ . If its height is $5 cm$ , find its volume and total surface area. [Use $π = 3.14$ ]

Important Questions on Surface Area and Volume

Learn and Prepare for any exam you want !

A hollow metal cylindrical disc is 3 cm thick and its external diameter is 14 cm. If its height is 5 cm, find its volume and total surface area. [Use π=3.14]

Important Questions on Surface Area and Volume

Learn and Prepare for any exam you want !

A hollow metal cylindrical disc is $3 cm$ thick and its external diameter is $14 cm$ . If its height is $5 cm$ , find its volume and total surface area. [Use $π = 3.14$ ]