To evaluate the expression \( \pi(42)^2 \cdot 40 \):

1. **Square the radius (42):**
   \[
   42^2 = 42 \times 42 = 1764
   \]

2. **Multiply by the height (40):**
   \[
   1764 \times 40 = 70560
   \]

3. **Multiply by \( \pi \):**
   \[
   \pi \times 70560 \approx 3.14159 \times 70560 \approx 221,689.44
   \]

So, the value of \( \pi(42)^2 \cdot 40 \) is approximately **221,689.44**.

Would you like to go into more detail or have any further questions?

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**Related Questions:**
1. How does this calculation relate to finding the volume of a cylinder?
2. What is the exact value in terms of \( \pi \) before approximating?
3. How does changing the radius affect the result?
4. Can this formula be used to find the surface area? If not, what would change?
5. How would the result change if the height was doubled?

**Tip:** When dealing with \( \pi \), it's often useful to leave your answer in terms of \( \pi \) for exact results unless a decimal approximation is specifically requested.

Learn how to calculate the volume of a cylinder with a radius of 42 units and a height of 40 units using the formula V = \pi r^2 h. This problem involves geometry and circle concepts, focusing on volume calculation. Suitable for students in Grades 9-12.

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