To find the volume of the wooden block after drilling a circular hole through it, we need to start by finding the volume of the entire wooden block and then subtracting the volume of the cylindrical hole.

Step 1: Volume of the Wooden Block

The volume $V$ of a rectangular block can be calculated using the formula: $V = \text{length} \times \text{width} \times \text{height}$ Given:

• Length = 30 cm
• Width = 20 cm
• Height = 10 cm

$V = 30 \times 20 \times 10 = 6000 \, \text{cm}^3$

Step 2: Volume of the Cylindrical Hole

The volume of a cylinder is calculated using the formula: $V_{\text{cylinder}} = \pi \times r^2 \times h$ where:

• $r$ is the radius of the hole, and
• $h$ is the height (or depth) of the hole through the block.

Since the diameter of the hole is 14 cm, the radius $r$ is: $r = \frac{14}{2} = 7 \, \text{cm}$ The depth of the hole, which corresponds to the height of the cylinder, is the same as the height of the block, so $h = 10$ cm.

Thus, the volume of the cylindrical hole is: $V_{\text{cylinder}} = \pi \times 7^2 \times 10 = \pi \times 49 \times 10 = 490\pi \, \text{cm}^3$

Using $\pi \approx 3.1416$: $V_{\text{cylinder}} \approx 490 \times 3.1416 \approx 1539.38 \, \text{cm}^3$

Step 3: Volume of the Wooden Block with the Hole

Now, subtract the volume of the hole from the volume of the entire block: $V_{\text{block with hole}} = 6000 - 1539.38 \approx 4460.62 \, \text{cm}^3$

Final Answer:

The volume of the wooden block after drilling the hole is approximately: $4460.62 \, \text{cm}^3$

Would you like further details on any part of the solution?

---

Here are some related questions for further exploration:

1. How would the volume change if the hole had a larger diameter?
2. What is the surface area of the hole within the block?
3. How would you find the weight of the block if the density of the wood were given?
4. How does drilling additional holes impact the structural integrity of the block?
5. What would be the volume if the hole didn’t go all the way through?

Tip: When working with shapes involving holes, remember to calculate the "removed" volume and subtract it from the total.