### 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 = π*r*^{ }^{2} × 8.1

103 =25.43 × *r*^{ }^{2}

4.05 ≈ *r*^{2}

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* = π*r*^{ }^{2} × 20.7

*V* =65 × *r*^{ }^{2}

*V* =65 × (3.45)^{2}

*V* ≈ 773.64 cm^{3}

**The volume of the cylinder is 773.64 cm**^{3}

### 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*

= π*r*^{ }^{2}*h*

=3.14 × (2.01)^{2}^{ }× 8.1

*V* ≈ 102.75 cm^{3}

**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:

1. _______________ is the measure of space inside a solid figure.

2. The volume of a cylinder is the product of the _______________ and the ________________.

3. Find the volume of the following cylinder

4. What two measurements do you need to know to find the volume of a cylinder?

5. What is the volume of a cylinder with a radius of 5 centimeters and a height of 2.5 centimeters? Use 3.14 for π.

6. The volume of a cylinder is 2257 cubic inches, and the height of the cylinder is 1 inch. What is the radius of the cylinder?

7. The cylinder shown has a volume of 885 cubic inches. What is the radius of the cylinder? Use 3.14 for π.

8. The volume of a cylinder is 1,029 cubic centimeters, and the height of the cylinder is 21 centimeters. What is the radius to the nearest centimeter of the cylinder?

9. The diameter of a cylinder is 7 yards. The height is 12 yards. What is the volume, in terms of π and to the nearest cubic yard, of the cylinder?

10. The volume of the cylinder is 400 cm^{3}. What is the height of the cylinder?

### 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.

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