Volume and Capacity

Grade 7 Math - Volume and Capacity

Lesson Objectives

Define and differentiate between volume and capacity.
Understand and apply units of measurement for volume and capacity.
Compare and convert different units of volume and capacity.

Lesson Introduction

Have you ever wondered how much liquid a container can hold or how to calculate the amount of space inside an object? In this lesson, we will explore how to measure and compare the volume and capacity of different shapes and objects. These concepts are used every day, from determining how much water a swimming pool can hold to figuring out how much liquid fits in a bottle!

Core Lesson Content

Volume refers to the amount of space inside a 3D object, and capacity refers to the amount a container can hold. In this section, we will learn how to calculate both and how to compare them.

Worked Examples

Example 1: Calculating the volume of a cube.

A cube has side length of 4 cm. To find its volume, use the formula:

$V = a^3$

Substituting the side length:

$V = 4^3 = 64 \, \text{cm}^3$

Example 2: Calculating the volume of a rectangular prism.

A rectangular prism has dimensions 5 cm by 3 cm by 2 cm. The volume is calculated as:

$V = l \times w \times h$

Substituting the values:

$V = 5 \times 3 \times 2 = 30 \, \text{cm}^3$

Example 3: Comparing the volumes of two containers.

Container A has a volume of 150 cm³, and Container B has a volume of 125 cm³. Which container holds more?

Since 150 cm³ > 125 cm³, Container A holds more.

Example 4: Converting from liters to milliliters.

Convert 3 liters to milliliters. We know that:

$1 \, \text{liter} = 1000 \, \text{milliliters}$

So,

$3 \, \text{liters} = 3 \times 1000 = 3000 \, \text{milliliters}$

Example 5: Calculating the volume of a cylinder.

The radius of a cylinder is 3 cm, and its height is 7 cm. The formula for the volume of a cylinder is:

$V = \pi r^2 h$

Substituting the values:

$V = \pi \times 3^2 \times 7 = 63\pi \, \text{cm}^3$

Example 6: Comparing volumes in different units.

Container A holds 0.5 liters, and Container B holds 500 milliliters. Which container holds more?

We know that 1 liter = 1000 milliliters. So:

$0.5 \, \text{liters} = 500 \, \text{milliliters}$

Therefore, both containers hold the same amount of liquid.

Example 7: Converting from milliliters to liters.

Convert 1500 milliliters to liters:

$1 \, \text{liter} = 1000 \, \text{milliliters}$

So:

$1500 \, \text{milliliters} = \frac{1500}{1000} = 1.5 \, \text{liters}$

Example 8: Volume of a sphere.

The radius of a sphere is 4 cm. The formula for the volume of a sphere is:

$V = \frac{4}{3} \pi r^3$

Substituting the radius:

$V = \frac{4}{3} \pi \times 4^3 = \frac{4}{3} \pi \times 64 = 85.33 \pi \, \text{cm}^3$

Example 9: Capacity of a tank.

If a tank has a volume of 2000 cm³, what is its capacity in liters?

$1 \, \text{liter} = 1000 \, \text{cm}^3$

So:

$2000 \, \text{cm}^3 = \frac{2000}{1000} = 2 \, \text{liters}$

Example 10: Capacity conversion between milliliters and liters.

If a container holds 2500 milliliters, what is its capacity in liters?

$1 \, \text{liter} = 1000 \, \text{milliliters}$

So:

$2500 \, \text{milliliters} = \frac{2500}{1000} = 2.5 \, \text{liters}$

Exercises

Calculate the volume of a cube with a side length of 5 cm.
[WAEC] Convert 2.5 liters to milliliters. [Past Question]
Find the volume of a cylinder with a radius of 6 cm and a height of 8 cm.
Calculate the capacity of a tank with a volume of 5000 cm³ in liters.
[NECO] The volume of a rectangular prism is 120 cm³. If the length is 6 cm and the width is 4 cm, what is the height of the prism? [Past Question]
A cylinder has a radius of 7 cm and a height of 10 cm. Calculate its volume.
[JAMB] Convert 750 milliliters to liters. [Past Question]
A tank is filled with 3 liters of water. How many milliliters of water does the tank hold?
[NABTEC] Calculate the volume of a sphere with a radius of 5 cm. [Past Question]
Compare the capacities of two containers, one with a capacity of 2000 milliliters and the other with a capacity of 2 liters. Which holds more?

Conclusion/Recap

Today, we learned about volume and capacity, how to calculate them, and how to convert between units. Understanding these concepts is essential for measuring space and the amount of liquid in containers. Next, we will explore surface area and its applications in geometry.