https://file.aiquickdraw.com/mathbot/file/1726917280774lf6dj69y.jpg

The image shows a cylinder with a diameter of **4 cm** and a height (or length) of **19 cm**. We are tasked with finding the volume of this cylinder:

The volume \( V \) of a cylinder is given by the formula:
\[
V = \pi r^2 h
\]
where:
- \( r \) is the radius of the base,
- \( h \) is the height (or length) of the cylinder,
- \( \pi \) is the constant Pi.

### Step 1: Calculate in terms of \( \pi \)
1. **Radius** \( r = \frac{4}{2} = 2 \) cm (since diameter = 4 cm).
2. **Height** \( h = 19 \) cm.

Now substitute these values into the formula:
\[
V = \pi (2)^2 (19) = \pi \times 4 \times 19 = 76\pi \, \text{cm}^3
\]

So, the volume in terms of \( \pi \) is:
\[
V = 76\pi \, \text{cm}^3
\]

### Step 2: Calculate the volume to two decimal places
Using \( \pi \approx 3.1416 \), we calculate:
\[
V = 76 \times 3.1416 = 238.76 \, \text{cm}^3
\]

### Final answers:
a) In terms of \( \pi \): \( 76\pi \, \text{cm}^3 \).

b) To two decimal places: \( 238.76 \, \text{cm}^3 \).

---

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What is the surface area of this cylinder?
2. How does changing the height affect the volume of a cylinder?
3. If the diameter of the cylinder were doubled, what would the new volume be?
4. How is the formula for the volume of a cylinder derived?
5. What is the relationship between volume and surface area for a cylinder?

**Tip:** Always ensure you use consistent units (e.g., cm, m) when calculating volume to avoid errors in interpretation.

Calculate the volume of this cylinder: a) in terms of pi, b) to 2 d.p.

Learn how to calculate the volume of a cylinder with a diameter of 4 cm and a height of 19 cm. Find the answer both in terms of pi and to two decimal places, using the formula V = πr^2h. This step-by-step guide is suitable for students in Grades 8-10.

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