Volume Of Cylinders – Concept and Explanation

Key Concepts

■ Relating volume of rectangular prisms and cylinders.

■ Find an unknown measure.

■ Solving problems involving volume of a cylinder.

Introduction:

Volume: 

The volume of a three-dimensional figure is the number of non-overlapping cubic units contained in the interior of the figure. Volume is measured in cubic units. 

For example, the prism below has a volume of 8 cubic centimeters. You can use this idea to develop volume formulas. 

Volume of a Cylinder: 

The volume V of a cylinder is the product of the base area B and the height h. 

V = Bh 

8.2.1 Relating Volume of Rectangular Prisms and Cylinders 

Example 1: 

Janice is buying a new fish tank for the growing population of zebrafish in her science lab. The tank needs to have a volume of 5200 cubic inches. How can Janice determine whether the cylindrical tank can hold the zebrafish? 

Solution: 

Use the formula to find the volume of the cylinder. Use 3.14 for π. 

8.2.2 Find an Unknown Measure 

Example 2: 

A company is designing a new cylindrical water bottle. The volume of the bottle is 103 cubic centimeters. What is the radius of the water bottle? Estimate using 3.14 for π, and round to the nearest tenth. 

Solution: 

Use the formula V = Bh to find the radius of the base of the bottle.  

V = Bh 

103 = πr ² × 8.1 

103 =25.43 × r ² 

4.05 ≈ r² 

2.01 ≈ r 

The radius of the bottle is about 2.01 centimeters. 

Example 3: 

Toy rubber balls are packed in a cylinder that holds 3 balls. Find the volume of the cylinder. Use 3.14 for π, and round to the nearest tenth. 

Solution: 

Use the formula V = Bh to find the volume of the cylinder.  

V = Bh 

V = πr ² × 20.7 

V =65 × r ² 

V =65 × (3.45)² 

V ≈ 773.64 cm³ 

The volume of the cylinder is 773.64 cm³ 

8.2.3 Solving Problems Involving Volume of a Cylinder 

Example 4: 

Terry uses a water bottle with the following dimensions. He wants to fill 500 cubic centimeters of water in such bottles. How many bottles are required? Use 3.14 for π. 

Solution: 

Step 1: 

Find the volume of the water bottle. 

V = Bh 

= πr ²h 

=3.14 × (2.01)² × 8.1 

V ≈ 102.75 cm³ 

Step 2: 

Find the number of bottles that can be filled. 

500/102.75

≈ 4.86 

Terry need 5 bottles to fill the water. 

Exercise:

Concept Map:

What have we learned:

• Calculate volume of cylinders.
• Find an unknown measure of cylinder.
• Solve problems involving volume of a cylinder in the given scenario.