Question

The circumference of the base of a cylinder is 22 cm and its height is 30 cm. Find the
volume of the cylinder, its curved surface area and total surface area.

Answer 1

Step-by-step explanation:

C=2πr

22=2*3.14*r

r=3.50

V=πr^2h

= 3.14*(3.50)^2 *30

=1153.95 cm

Curved surface = 2πrh

=2*3.14*3.50*30 =659.4 cm^2

Total surface area=2πr (h + r)

=2*3.14* 3.50 (30*3.50) =2307.9 cm^2

Answer 2

Given:

The circumference of the base of a cylinder = 22 cm

Height = 30 cm

To find :

The volume of the cylinder

Curved surface area of a cylinder

Total surface area of a cylinder

Formula to be used:

Volume of a cylinder = πr²h

Curved surface area of a cylinder = 2πrh

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

Solution:

Step 1 of 3:

Let 'r' be the radius of cylinder.

Circumference of the base of a cylinder, 2πr = 22 cm

2 × $\frac{22}{7}$ × r = 22

2 × r = 22 × $\frac{7}{22}$

2 × r = 7

r = $\frac{7}{2}$

r = 3.5

Volume of a cylinder = πr²h

Volume of a cylinder =  $\frac{22}{7}$ × (3.5)² × 30

Volume of a cylinder =  3.14 × 12.25 × 30

Volume of a cylinder = 11,53.95 cm³

Step 2 of 3:

Curved surface area of a cylinder = 2πrh

2πr = 22 cm, h = 30 cm

Curved surface area of a cylinder = 22 × 30

Curved surface area of a cylinder = 660 cm²

Step 3 of 3:

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

2πr = 22 cm, h = 30 cm, r = 3.5

Total surface area of a cylinder = 22 (30 + 3.5)

Total surface area of a cylinder = 22 (33.5)

Total surface area of a cylinder = 737 cm²

Final answer:

Volume of the cylinder is 11,53.95 cm³

Curved surface area ofa  cylinder is 660 cm²

Total surface area of a cylinder is 737 cm²