Question

The volume of this cylinder is 16,334.28 cubic feet. What is the height?

Use ​𝜋 ≈ 3.14 and round your answer to the nearest hundredth.
radius is 17ft

Answer 1

907.46 not 908.06

Answer 2

are u sure?.. i got 4.2426 round that to the nearest hundreth

Answer 3

To find the height of a cylinder given its volume, we can use the formula for the volume of a cylinder:

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

Where:
- \( V \) is the volume of the cylinder,
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.

Given:
- Volume \( V = 16,334.28 \) cubic feet,
- Radius \( r = 17 \) feet,
- \( \pi \approx 3.14 \).

Now, we can rearrange the formula to solve for the height \( h \):

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

First, calculate \( r^2 \):

\[
r^2 = 17^2 = 289
\]

Now, calculate \( \pi r^2 \):

\[
\pi r^2 = 3.14 \times 289 \approx 908.06
\]

Now, we can calculate the height \( h \):

\[
h = \frac{16,334.28}{908.06} \approx 17.99
\]

Rounding to the nearest hundredth, the height of the cylinder is:

\[
\boxed{17.99} \text{ feet}
\]

Answer 4

Let's recalculate \( \pi r^2 \) correctly.

Given:
- \( r = 17 \) feet
- \( \pi \approx 3.14 \)

First, we calculate \( r^2 \):
\[
r^2 = 17^2 = 289
\]

Now, calculate \( \pi r^2 \):
\[
\pi r^2 = 3.14 \times 289
\]

Calculating that:
\[
\pi r^2 = 3.14 \times 289 = 907.46
\]

Now that we have \( \pi r^2 = 907.46 \), we can find the height \( h \) using the volume formula:
\[
h = \frac{V}{\pi r^2}
\]
Substituting in the values:
\[
h = \frac{16,334.28}{907.46}
\]

Calculating \( h \):
\[
h \approx 17.99
\]

So, after correcting the \( \pi r^2 \) calculation, the height still comes out to be approximately:
\[
\boxed{17.99} \text{ feet}
\]

Thank you for your patience and the correction!

Answer 5

Let's recalculate the height step by step to clarify:

**Given:**
- Volume \( V = 16,334.28 \) cubic feet
- Radius \( r = 17 \) feet
- \( \pi \approx 3.14 \)

### Step 1: Calculate \( r^2 \)
\[
r^2 = 17^2 = 289
\]

### Step 2: Calculate \( \pi r^2 \)
\[
\pi r^2 = 3.14 \times 289 \approx 907.46
\]

### Step 3: Calculate height \( h \)
Using the formula for height:
\[
h = \frac{V}{\pi r^2} = \frac{16,334.28}{907.46}
\]

### Performing the Calculation for Height
\[
h \approx \frac{16,334.28}{907.46} \approx 17.99
\]

### Step 4: Rounding
So, the height \( h \approx 17.99 \) feet when rounded to the nearest hundredth.

If you have computed it and got approximately \( 4.2426 \), it might be due to using a different volume or values in the formula. Please check the inputs to ensure you’re calculating with the same volume and radius.

Can you clarify if you have a different volume or radius in mind? Based on information provided, the height should be approximately \( 17.99 \) feet.