Question 4

We need to find the volume of wood by subtracting the volume of the conical depressions from the cuboid's volume.

Step 1 — Calculate the volume of the cuboid

First, let's find the volume of the entire wooden cuboid. The cuboid has a length of 15 cm, a breadth of 10 cm, and a height of 3.5 cm. The formula for the volume of a cuboid is $l \times b \times h$.

$V_{\text{cuboid}} = 15 \text{ cm} \times 10 \text{ cm} \times 3.5 \text{ cm}$

$= 525 \text{ cm}^3$

$\boxed{V_{\text{cuboid}} = 525 \text{ cm}^3}$

Step 2 — Calculate the volume of one conical depression

Next, let's find the volume of a single conical depression. Each depression has a radius ($r$) of 0.5 cm and a depth ($h$) of 1.4 cm. The formula for the volume of a cone is $1/3 \times \pi \times r^2 \times h$.

$V_{\text{cone}} = \frac{1}{3} \times \frac{22}{7} \times (0.5 \text{ cm})^2 \times 1.4 \text{ cm}$

$= \frac{1}{3} \times \frac{22}{7} \times 0.25 \text{ cm}^2 \times 1.4 \text{ cm}$

$= \frac{1}{3} \times 22 \times 0.25 \times 0.2 \text{ cm}^3$

$= \frac{1}{3} \times 1.1 \text{ cm}^3$

$= \frac{1.1}{3} \text{ cm}^3$

$\boxed{V_{\text{cone}} \approx 0.3667 \text{ cm}^3}$

Step 3 — Calculate the total volume of four conical depressions

There are four such conical depressions in the pen stand. We multiply the volume of one cone by 4.

$V_{\text{total depressions}} = 4 \times V_{\text{cone}}$

$= 4 \times \frac{1.1}{3} \text{ cm}^3$

$= \frac{4.4}{3} \text{ cm}^3$

$= 1.4666... \text{ cm}^3$

$\boxed{V_{\text{total depressions}} \approx 1.47 \text{ cm}^3}$

Step 4 — Calculate the volume of wood in the stand

Finally, we subtract the total volume of the depressions from the volume of the cuboid. This will give us the volume of the remaining wood.

$V_{\text{wood}} = V_{\text{cuboid}} - V_{\text{total depressions}}$

$= 525 \text{ cm}^3 - 1.4666... \text{ cm}^3$

$= 523.5333... \text{ cm}^3$

$\boxed{V_{\text{wood}} \approx 523.53 \text{ cm}^3}$

Answer

The volume of wood in the entire stand is approximately 523.53 cm³.