**Surface Area of a
Cylinder**

A right circular **cylinder **is a
solid shape with two parallel circular end faces and a uniform circular cross-section.
Each end face is called the base of the cylinder. The radius of the cylinder is
called the **base radius**. The perpendicular distance between the two bases
is called the **height **of the cylinder.

Consider a hollow cylinder made of
paper. Now, cut the curved surface of the cylinder along a line parallel to the
axis of the cylinder and unfold it. It will give you the shape of a rectangle.

Now, the length of the rectangle = circumference
of circular end = 2π*r*

Breadth of the rectangle = height of
the cylinder = *h*

Curved surface area of the cylinder =
Area of the rectangle

= Length × breadth

= 2π*r* × *h*

= 2π*rh *sq. units

**Curved
surface area of a cylinder = 2π rh**

Now, the total surface area of cylinder
= Curved surface area + Area of two circular bases

= 2π*rh*
+ 2π*r*^{2}

= 2π*r*(*h*
+ *r*) sq. units

**Total
surface area of a cylinder = 2π r(h + r)**

**Surface Area of a
Cylinder Formula**

**Curved
surface area of a cylinder = 2π rh**

**Total
surface area of a cylinder = 2π r(h + r)**

**Surface Area of a
Hollow Cylinder Formula**

Curved surface area of a hollow
cylinder = External surface area + Internal surface area

= 2πR*h *+ 2π*rh *= 2π*h*(R + *r*) sq. units

Surface area of each base = πR^{2}
– π*r*^{2} = π(R^{2} – *r*^{2}) sq. units

Total surface area of a hollow
cylinder = Curved surface area + Surface area of two circular bases

= 2π*h*(R + *r*)
+ 2π(R^{2} – *r*^{2})

= 2π*h*(R + *r*) + 2π (R + *r*) (R – *r*)

= 2π(R + *r*) (*h *+ R – *r*) sq. units

**Curved
surface area of a hollow cylinder = 2π h(R + r)**

**Total
surface area of a hollow cylinder = 2π(R + r) (h + R – r)**

Where R is the external radius, *r*
is the internal radius and *h* is the height of the hollow cylinder.

**Surface Area of a
Cylinder Examples**

**Example 1: **The base radius of a solid
cylinder is 7 cm and its height is 12 cm. Find the total surface area of the
cylinder.

**Solution: **We have, the base radius (*r*)*
*= 7 cm and height (*h*)* *= 12 cm

Total
surface area of the cylinder = 2π*r*(*h *+ *r*)

= 2 × 22/7 × 7 (12 + 7)

= 836 cm^{2}

**Example 2: **Find
the curved surface area of a cylinder whose base radius is 28 cm and height is
20 cm.

**Solution:**
Given: Radius (*r*) = 28 cm, Height (*h*) = 20 cm

Surface area of the cylinder = 2π*rh
*sq. units

= 2 × 22/7 × 28 × 20

= 3520 sq. cm

**Example 3: **Find
the total surface area of a hollow cylinder whose external and internal radii
are 9 cm and 5 cm, respectively and its height is 24 cm.

**Solution: **Given: External radius (R) = 9 cm, internal
radius (*r*)* *= 5 cm, *h *= 24 cm

Total surface area of the hollow
cylinder = 2π(R + *r*)(*h *+ R – *r*)

= 2 × 22/7 × (9 + 5) × (24 + 9 – 5)

=
2 × 22/7 × 14 × 28

= 2464 sq. cm