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 = 2πr
Breadth of the rectangle = height of
the cylinder = h
Curved surface area of the cylinder =
Area of the rectangle
= Length × breadth
= 2πr × h
= 2πrh sq. units
Curved
surface area of a cylinder = 2πrh
Now, the total surface area of cylinder
= Curved surface area + Area of two circular bases
= 2πrh
+ 2πr2
= 2πr(h
+ r) sq. units
Total
surface area of a cylinder = 2πr(h + r)
Surface Area of a Cylinder Formula
Curved
surface area of a cylinder = 2πrh
Total
surface area of a cylinder = 2πr(h + r)
Surface Area of a Hollow Cylinder Formula
Curved surface area of a hollow
cylinder = External surface area + Internal surface area
= 2πRh + 2πrh = 2πh(R + r) sq. units
Surface area of each base = πR2
– πr2 = π(R2 – r2) sq. units
Total surface area of a hollow
cylinder = Curved surface area + Surface area of two circular bases
= 2πh(R + r)
+ 2π(R2 – r2)
= 2πh(R + r) + 2π (R + r) (R – r)
= 2π(R + r) (h + R – r) sq. units
Curved
surface area of a hollow cylinder = 2πh(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 = 2πr(h + r)
= 2 × 22/7 × 7 (12 + 7)
= 836 cm2
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 = 2πrh
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