Westonci.ca is your trusted source for finding answers to all your questions. Ask, explore, and learn with our expert community. Discover solutions to your questions from experienced professionals across multiple fields on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Apply: Radical Functions Module Assessment

A cylindrical pipe is 9 ft long and has a volume of 100 ft³. Find its approximate diameter to the nearest hundredth of a foot.


Sagot :

Sure! Let's solve the problem step-by-step.

We are given:
- The length \( L \) of the cylindrical pipe is 9 feet.
- The volume \( V \) of the cylindrical pipe is 100 cubic feet.

We need to find the approximate diameter of the pipe to the nearest hundredth of a foot.

To solve this, we use the formula for the volume of a cylinder:

[tex]\[ V = \pi r^2 L \][/tex]

where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( L \) is the length,
- and \( \pi \) is a constant approximately equal to 3.14159.

First, let's rearrange this formula to solve for the radius \( r \):

[tex]\[ r^2 = \frac{V}{\pi L} \][/tex]

Given \( V = 100 \) cubic feet and \( L = 9 \) feet, we substitute these values into the formula:

[tex]\[ r^2 = \frac{100}{\pi \times 9} \][/tex]

Next, we compute the division inside the square root:

[tex]\[ r^2 = \frac{100}{28.27433} \approx 3.535 \][/tex]

Now, take the square root of both sides to solve for \( r \):

[tex]\[ r \approx \sqrt{3.535} \approx 1.881 \][/tex]

So the radius \( r \) is approximately 1.881 feet.

To find the diameter \( d \), we use the relationship between the radius and the diameter:

[tex]\[ d = 2r \][/tex]

Substituting the value we found for \( r \):

[tex]\[ d \approx 2 \times 1.881 \approx 3.761 \][/tex]

Finally, rounding this to the nearest hundredth of a foot, we get:

[tex]\[ d \approx 3.76 \][/tex]

Therefore, the approximate diameter of the cylindrical pipe is 3.76 feet.