Surface Area of a Cylinder Formula

# Surface Area of a Cylinder Formula

## 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

= 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(R2r2) sq. units

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

= 2πh(R + r) + 2π(R2r2)

= 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