Given V=𝚷r2h and V=2410,r=12, find h correct to 1 d.p.

Given the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

We are provided with:

\[
V = 2410, \quad r = 12
\]

We need to find the height \( h \) correct to 1 decimal place.

First, let's rearrange the formula to solve for \( h \):

\[
h = \frac{V}{\pi r^2}
\]

Substituting the values given:

\[
h = \frac{2410}{\pi \times 12^2}
\]

Now, calculating \( h \):

\[
h = \frac{2410}{\pi \times 144} \approx \frac{2410}{452.3893} \approx 5.325
\]

So, the height \( h \) correct to 1 decimal place is:

\[
\boxed{5.3}
\]

Would you like more details, or have any questions?

Here are some related questions:
1. How does the height of the cylinder change if the radius is doubled?
2. What would be the volume if the height was 10 and the radius remained 12?
3. How does the volume change if both the height and radius are doubled?
4. What is the surface area of the cylinder given the radius and height?
5. How do we derive the formula for the volume of a cylinder?

**Tip:** Remember that the volume of a cylinder scales with the square of the radius, meaning small changes in radius significantly affect the volume.

Learn how to calculate the height of a cylinder given its volume and radius. Follow a step-by-step solution using the formula V = π r^2 h. Practice solving for h with provided values V = 2410 and r = 12, ensuring precision to 1 decimal place.

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