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Important Question

A cylinder is a 3d shaped object. It has two parallel circular bases at each end of the cylindrical shape. The line which joins the center of these circular bases is known as the axis.

The distance between the axis and the other half of the outer part is known as the radius of the cylinder. The distance between both the circular bases is the height of the cylinder.

There are many examples of cylindrical shaped objects which we use in our daily life. They are Pipe, Candles, Tank, Well, etc. Let’s now dive deeper into what is surface area, the curved surface area of a cylinder, the formula used in it, and the derivation of the formula.

We will also have a look at some of the examples where we will use the concept of curved surface area.

The outside part or covering of any object is known as the surface. Similarly, the outer part of any cylindrical-shaped object is its surface area.

A cylinder has two types of surfaces in it. One is the curved surface and the other is circular. The area and the diameter of both the circular areas are the same.

Also Read: Lens Formula.

We have two types of surface areas in cylindrical objects. Two of them are listed below.

- Curved Surface Area (C.S.A)
- Total Surface Area (T.S.A)

Let’s read on to find more about the two types of cylindrical surface areas.

The area of the curved surface of the cylinder is known as the curved surface area. It can also be obtained after excluding the circular area from the total area of the cylinder. This is the reason for being known as Lateral surface area.

Do you know the value of Cos 60?

Lateral surface area is the remaining area obtained from an object by excluding the top and the bottom part of it.

If we consider the height of the cylinder as ‘h’, and the radius of the cylinder to be ‘r’, then we have the formula of c.s.a of a cylinder as

**2*pi*r*h square units.**

The total surface area of a cylinder is the sum of all the surfaces. As we have mentioned previously that a cylinder has two types of surfaces, curved and circular. So, the addition of both of these gives us the total surface area of a cylinder.

**T.S.A = C.S.A. + Area of circular bases.**

Also Read the table of 14.

If we consider the height as ‘h’ and radius as ‘r’, then the formula for total surface area is given by

**T.S.A = C.S.A. + Area of circular bases.**

**T.S.A= 2*pi*r*h + 2*pi*r*r**

The area of a cylinder is the area of the circles whose base radius is ‘r’ and the area of the curved surface.

The height of the rectangle is *h*, while the length of the rectangle is the circumference of the circle. The area of the rectangle is the **curved surface area of the cylinder = 2πrh.**

Hence, **total surface area of the cylinder = 2πr2+2πrh**

** = 2πr(h+r)**

You can also have a look at the Table of 25

Subham has given a cylinder of surface area 1880 pi square units. Find the height of the cylinder if the radius of the base of the circle is 24 units.

**Solution:**

The surface area of the cylinder, A = 1880 pi

Using the area of the base is: A = 2*pi*r(h+r)

1880 pi = 2 pi ×24 ×(h+24)

⇒ 1880/48 = (h+24)

⇒ 39.166 = h + 24

⇒ h = 15.166

So, the height of the cylinder is 15 units.

**What is the formula of curved surface area?**

The area obtained after excluding the circular area from the total area of the cylinder is known as curved surface area. Curved surface area is given by 2 * pi *r * h.

**What is the slant height?**

The height of a triangle comprising of a lateral face is the slant height.

**What is a formula for slant height?**

The formula for slant height is given by a^2+b^2=c^3

**What is the curved surface?**

The curved surface is a rounded surface that is not flat.

The area obtained after excluding the circular area from the total area of the cylinder is known as curved surface area. Curved surface area is given by 2 * pi *r * h.

The height of a triangle comprising of a lateral face is the slant height.

The formula for slant height is given by a^2+b^2=c^3

The curved surface is a rounded surface that is not flat.

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