A cylinder is a 3-D geometry with two circular surfaces and one curved surface. Let us know how the surface area of a cylinder or circumference is determined. Cylinder has height and radius. The cylinder has two bases, the base has radius r.

Formula for finding circumference of a cylinder.

Circumference of cylinder = 2 x ? x r(r + h)

**Example problems for circumference of a cylinder**

**Example 1:** Find the circumference of a cylinder whose radius = 5cm and height = 7cm

**Solution:**

Circumference of cylinder = 2 ? r (r + h)

= 2 x 3.14 × 5(r + h)

= 2 x 3.14× 5(5 + 7)

= 6.28 × 5(12)

= 376.8

**Example 2:** Find the circumference of a cylinder whose radius = 5.5 cm and height = 9cm

**Solution:**

Circumference of cylinder = 2 ? r (r + h)

= 2 x 3.14 ×5.5(5.5 + 9)

= 2 x 3.14 ×5.5(14.5)

= 6.28 × 79.75

= 500.83

**Example 3:** Find the circumference of a cylinder whose radius = 9cm and height = 6cm

**Solution:**

Circumference of cylinder = 2 ? r (r + h)

= 2 x 3.14 × 9(9 + 6)

= 6.28 × 9 (15)

= 6.28 ×135

= 847.8

**Example 4:** Find the circumference of a cylinder whose radius = 11 cm and height = 4.9cm

**Solution:**

Circumference of cylinder = 2 ? r (r + h)

= 2 x 3.14 × r(r + h)

= 2 x 3.14 × 11(11 + 4.9)

= 6.28 × 11(15.9)

= 6.28 × 174.9

=1098.37

**Example 5:** Find the radius of the cylinder whose circumference is 75.36 and height is 7cm

** Solution:**

Circumference of cylinder = 75.36

2 ? r(r + h) = 75.36

6.38 × r(r + 7) = 75.36

r^{2} + 7r = 11.812

r = ±?b^{2}-4ac/2a

a= 1, b= 7, c= -11.812

r = ± ?49 + 47.248/2

r = ±?96.248/2

r = ±9.81/2

r= ± 4.91

Since radius is not in negative so radius r =4.91

4.91 is round to the nearest round value Therefore r =5cm.

**Practicing problems**

1) Find the circumference of a cylinder whose height h =12cm and radius r= 2cm?

2) Radius r = 6cm and height h= 10 cm find the lateral surface area or circumference of a cylinder?

3) Find the circumference of a cylinder, radius r = 12 and height h = 18?

**Answers:**

1) 175.84

2) 602.88

3)2260.8