How many bricks each of size 30 cm by 18 cm by 12 cm will be required to fill a pit of 6 m by 3.6 m by 60 cm?


To find the number of bricks required to fill the pit, we need to calculate the volume of the pit and the volume of a single brick. Then, divide the volume of the pit by the volume of one brick.

### Step 1: Convert all dimensions to the same unit
We will convert all measurements to centimeters (cm).

- Dimensions of the pit:
  - Length = 6 meters = \( 6 \times 100 = 600 \, \text{cm} \)
  - Width = 3.6 meters = \( 3.6 \times 100 = 360 \, \text{cm} \)
  - Depth = 60 cm (already in cm)

So, the pit's dimensions are 600 cm by 360 cm by 60 cm.

- Dimensions of the brick:
  - Length = 30 cm
  - Width = 18 cm
  - Height = 12 cm

### Step 2: Calculate the volume of the pit
The volume of the pit is given by the formula for the volume of a rectangular prism:

\[
\text{Volume of the pit} = \text{Length} \times \text{Width} \times \text{Depth}
\]

\[
\text{Volume of the pit} = 600 \, \text{cm} \times 360 \, \text{cm} \times 60 \, \text{cm} = 12,960,000 \, \text{cm}^3
\]

### Step 3: Calculate the volume of one brick
The volume of a brick is also given by the same formula:

\[
\text{Volume of a brick} = 30 \, \text{cm} \times 18 \, \text{cm} \times 12 \, \text{cm} = 6,480 \, \text{cm}^3
\]

### Step 4: Calculate the number of bricks
Now, divide the volume of the pit by the volume of one brick:

\[
\text{Number of bricks} = \frac{\text{Volume of the pit}}{\text{Volume of one brick}} = \frac{12,960,000 \, \text{cm}^3}{6,480 \, \text{cm}^3}
\]

\[
\text{Number of bricks} = 2,000
\]

Thus, 2,000 bricks will be required to fill the pit.

Would you like further details or have any questions?

Here are 5 related questions to expand the understanding:
1. How would the result change if the dimensions of the bricks were different?
2. How can we account for mortar gaps between the bricks in the calculation?
3. What if the pit has a different shape, like a cylinder or a trapezoidal prism?
4. How would you convert the result if the bricks were measured in cubic feet rather than cubic centimeters?
5. What is the total surface area of the pit, and how can it help with material estimation?

**Tip**: When calculating volumes, ensure all units are consistently in the same measurement system before proceeding.

How many bricks each of size 30 cm by 18 cm by 12 cm will be required to fill a pit of 6 m by 3.6 m by 60 cm?

Find out how to calculate the number of bricks required to fill a pit with dimensions 6m by 3.6m by 60cm using volume calculation and unit conversion. Understand key geometry concepts and apply formulas to solve this problem. Suitable for students in Grades 6-8.

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