Sample Problems on Volume and Surface Area of a Cylinder

Problem 1: Compute the total surface area of the cylinder, with a radius of 5cm and height of 10cm?

Solution:

Since, we know, 

Total surface area of a cylinder, A = 2πr(r+h) square units

Therefore, A = 2π × 5(5 + 10) = 2π × 5(15) 

= 2π × 75 = 150 × 3.14 

= 471 cm²

Problem 2: What is the volume of a cylindrical shape water container, that has a height of 7cm and diameter of 10cm?

Solution: 

Given,

Diameter of the container = 10cm

Thus, radius of the container = 10/2 = 5cm

Height of container = 7cm

As we know, from the formula,

Volume of a cylinder = πr²h cubic units.

Therefore, volume of given container, V = π × 52 × 7

V = π × 25 × 7 = (22/7) × 25 × 7 = 22 × 25

V = 550 cm³

Problem 3: Alex wants to purchase a cylindrical can with a radius equivalent to 5 inches. The can contains 1 gallon of oil. Find the height of the cylinder. 

Solution:

Volume V is given by= 1 gallon

1 gallon= 231 cubic inches

Radius r = 5 inches

Volume f the cylinder is given by, 

 V = πr²h

231 = 22/7 × (5)² × h

(231 × 7)/(22 × 25) = h

h = 2.94 inches.

Therefore, the height is equivalent to 2.94 inches.

Problem 4: A water tank has a radius of 40 inches and a height of 150 inches. Find the area. 

Solution:

Water tank is cylindrical in nature. 

Total Surface Area of a cylinder is given by,  2πr(h+r)

TSA = 2 × 22/7 × 40(150 + 40)

TSA = 2 × 22/7 × 40 × 190

TSA = 440/7 × 7600

TSA = 3344000/ 7

Area = 47,7142.857 sq.inches.

Problem 5: Find the volume of the cylinder having a radius of 5 units and a height of 8 units?

Solution:

We have, 

Radius,r = 5 units

Height,h = 8 units

Volume of the cylinder, V = πr²h cubic units.

V = (22/7) × 5² × 8

V = 22/7 × 25 × 8

V= 628.57 Cubic units.

Hence, the volume of the cylinder is 628.57 cubic units.

The volume of a cylinder can be calculated using the formula V = πr²h. While the total surface area of a cylinder can be calculated using the formula: A=2πr(h+r). In geometry, a cylinder is a three-dimensional solid figure which contains two parallel circular bases joined by a curved surface, situated at a particular distance from the center of the cylinder.

For instance, toilet paper rolls, and plastic cold drink cans are examples of cylinders. A cylinder is characterized by two major properties, i.e. surface area and volume. The word cylinder is derived from a Latin (Cylindrus) word, meaning “roll”, “roller”, and “Tumblr”.