Skip to main content

Grade 10 Mathematics Teachers’ Book

INNODEMS

Subsection 2.8.1 (*) Volume of Cubes and Cuboids

\(\textbf{Volume}\) is the geometric space occupied by an object, or the contents of an object. It is measured in \(\textbf{cubic units}\text{.}\)
🔗
Computation of a volume is achieved by multiplying the area of the base of the solid by the height of the solid
🔗

Learner Experience 2.8.1.

Demonstrating how volume can be measured in real life situations.
🔗
  • Materials Needed:
    🔗
    • Water, sand or rice.
      🔗
    • Rulers
      🔗
    • Measuring cups
      🔗
    • Transparent boxes or cubical containers of different sizes.
      🔗
    • (You can take a cuboid-shaped Jerrycan; cut the top to ensure it has a flat top and base)
      🔗
    • Notebook and pen for recording findings and computing sums.
      🔗
    🔗
  1. Measure and record the units for height, length and width of the container.
    🔗
    Slowly fill the box (or container) with water, sand or rice.
    🔗
    Measure how many cups are needed to fill the box completely.
    🔗
    🔗
  2. What’s the mass of the rice, sand or water that filled the cubical container? Convert to cubic centimetres. Note down your answer.
    🔗
    Calculate the volume using the formula \(l \times w \times h\)
    🔗
    🔗
  3. Compare the actual measurement with your calculations.
    🔗
    🔗
🔗
NOTE Slight differences may occur due to gaps in sand, spills while transferring or measuring.
🔗
🔗

Key Takeaway 2.8.2.

The volumes of a cube with side length \(s\) is given by \(V = s^3\text{.}\)
🔗
The volume of a cuboid with length \(l\text{,}\) width \(w\) and height \(h\) is given by \(V = l \times w \times h\text{.}\)
🔗
🔗

Example 2.8.3.

Find the volume of the following cube whose side is \(5\, \text{cm}.\)
🔗
Solution.
Step 1: Find the area of the base
\begin{align*} \text{Area of square} = \amp S^2\\ = \amp 5^2\\ = \amp 25 \, \text{cm}^2 \end{align*}
🔗
Step 2: Multiply the area of the base by the height of the solid to find the volume
\begin{align*} \text{volume} = \amp \text {areaof base} \times \text{height}\\ = \amp 25 \, \text{cm}^2 \times 5 \, \text{cm}\\ = \amp 125 \, \text{cm}^3 \end{align*}
🔗
The volume of the cube is \(125 \, \text{cm}^3\text{.}\)
🔗
🔗
🔗

Example 2.8.4.

A cuboid has a length of 12 cm, a width of 8 cm, and a height of 5 cm. Find its volume.
🔗
🔗

Example 2.8.5.

Find the volume of a cuboid with base \(6 \times 4\) units and height \(8\) units.
🔗
Solution.
Base area = \(6 \times 4 = 24\ \text{units}^2\)
🔗
Volume = \(24 \times 8 = 192\ \text{units}^3\)
🔗
🔗
🔗

Checkpoint 2.8.6.

🔗

Checkpoint 2.8.7.

🔗

Exercises Exercises

1.

Find the volume of the following cube whose side is \(5\, \text{cm}.\)
🔗
Answer.
\(125 \, \text{cm}^3\)
🔗
🔗
🔗

2.

A cube has a side length of \(12 \, \text{cm}\text{.}\) Find its volume.
🔗
Answer.
\(1728 \, \text{cm}^3\)
🔗
🔗
🔗

3.

The cube below has a volume of \(343 \, \text{cm}^3\text{.}\) Find the length of one side of the cube.
🔗
Answer.
\(7 \, \text{cm}\)
🔗
🔗
🔗

4.

If the side length of a cube is doubled, by what factor does the volume increase?
🔗
Answer.
\(8\)
🔗
🔗
🔗

5.

A big cube is made by stacking \(8\) smaller identical cubes together. If the volume of each small cube is \(27 \, \text{cm}^3\text{,}\) find the volume of the big cube.
🔗
Answer.
\(216 \, \text{cm}^3\)
🔗
🔗
🔗

6.

  1. A cubical water tank is \(1 \, \text{m}\) on each side. How many liters of water can it hold when full?
    🔗
  2. A cubical water tank is \(2 \, \text{m}\) on each side. If it is filled completely, how many liters of water can it hold?
    🔗
🔗
Answer.
  1. \(\displaystyle 1,000 \, \text{liters}\)
    🔗
  2. \(\displaystyle 8,000 \, \text{liters}\)
    🔗
🔗
🔗
🔗

7.

A sugar cube has a side length of \(1 \, \text{cm}\text{.}\) If \(1,000\) sugar cubes are stacked together to form a larger cube, find the volume of the larger cube.
🔗
Answer.
\(1,000 \, \text{cm}^3\)
🔗
🔗
🔗

8.

A freezer contains \(200\) ice cubes, each shaped like a cube with a side length of \(4 \, \text{cm}\text{.}\) Find the total volume of ice inside the freezer.
🔗
Answer.
\(12,800 \, \text{cm}^3\)
🔗
🔗
🔗

9.

A cubical shipping container has a side length of \(2.5 \, \text{m}\text{.}\) Find the total volume of cargo space inside the container.
🔗
Answer.
\(15.625 \, \text{m}^3\)
🔗
🔗
🔗

10.

A cuboid has base \(5 \times 3\) units and height \(10\) units. Find its volume.
🔗
Answer.
\(150 \, \text{units}^3\text{.}\)
🔗
🔗
🔗

11.

A cuboid has base \(8 \times 2.5\) metres and height \(6\) metres. Find its volume in \(m^3\text{.}\)
🔗
Answer.
\(120 \, m^3\text{.}\)
🔗
🔗
🔗

12.

A warehouse floor has area \(250 \, \text{m}^2\text{.}\) If goods are stacked vertically to a height of \(4 \, \text{m}\text{,}\) find the total storage volume available.
🔗
Answer.
\(1000 \, \text{m}^3\text{.}\)
🔗
🔗
🔗

13.

A rectangular swimming pool is \(12 \, \text{m}\) long, \(5 \, \text{m}\) wide and \(2 \, \text{m}\) deep. Find the volume of water the pool can hold.
🔗
Answer.
\(120 \, \text{m}^3\text{.}\)
🔗
🔗
🔗

14.

A packing box has volume \(360 \, \text{cm}^3\) and base area \(15 \, \text{cm}^2\text{.}\) Find its height.
🔗
Answer.
\(24 \, \text{cm}\text{.}\)
🔗
🔗
🔗

15.

A crate measures \((x + 2)\) cm by \((x + 3)\) cm by \(5\) cm. Form an expression for its volume.
🔗
Answer.
\((x + 2)(x + 3)(5) \, \text{cm}^3\text{.}\)
🔗
🔗
🔗

16.

A cuboid has a volume of 600 cm³, a length of 10 cm, and a width of 5 cm. Find its height.
🔗
🔗

17.

A rectangular water tank has a base of 2 m by 3 m and a height of 4 m. How many liters of water can it hold when full?
🔗
🔗

18.

A shipping company uses boxes shaped like cuboids. Each box has a length of 40 cm, width of 30 cm, and height of 20 cm. If a warehouse has a storage space of 12 m³, how many such boxes can fit in the warehouse?
🔗
🔗

19.

If the length, width, and height of a cuboid are all doubled, by what factor does the volume increase?
🔗
🔗

20.

A brick has dimensions 20 cm by 10 cm by 5 cm. A wall is built using 500 such bricks, with no gaps between them. Find the total volume of bricks used in constructing the wall.
🔗
🔗

21.

A wooden storage box has a length of 1.2 m, a width of 80 cm, and a height of 50 cm. Find the volume of the box in cubic meters.
🔗
(Hint: Convert all dimensions to meters before calculating.)
🔗
🔗
🔗
🔗
PrevTopNext