Thank you for visiting The volume of a cylinder varies jointly with the square of its radius and with its height tex V k r 2 h tex Cylinder. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
To solve this question, we need to find the volume of cylinder B using the relationship provided for the volume of a cylinder, which varies jointly with the square of its radius and its height. The formula given is:
[tex]\[ V = k \cdot r^2 \cdot h \][/tex]
1. Determine the constant [tex]\( k \)[/tex] using Cylinder A:
- Cylinder A has a volume ([tex]\( V \)[/tex]) of 254.34 cubic inches, a radius ([tex]\( r \)[/tex]) of 3 inches, and a height ([tex]\( h \)[/tex]) of 9 inches.
- Substitute these values into the formula to solve for [tex]\( k \)[/tex]:
[tex]\[ 254.34 = k \cdot 3^2 \cdot 9 \][/tex]
[tex]\[ 254.34 = k \cdot 9 \cdot 9 \][/tex]
[tex]\[ 254.34 = k \cdot 81 \][/tex]
- Divide both sides by 81 to find [tex]\( k \)[/tex]:
[tex]\[ k = \frac{254.34}{81} \][/tex]
2. Calculate the volume of Cylinder B:
- Cylinder B has a radius ([tex]\( r \)[/tex]) of 4 inches and a height ([tex]\( h \)[/tex]) of 5 inches.
- Use the same formula to calculate the volume ([tex]\( V \)[/tex]) for Cylinder B:
[tex]\[ V = k \cdot 4^2 \cdot 5 \][/tex]
[tex]\[ V = k \cdot 16 \cdot 5 \][/tex]
[tex]\[ V = k \cdot 80 \][/tex]
3. Substitute the value of [tex]\( k \)[/tex] from the first step into the formula for Cylinder B:
- Given that [tex]\( k \approx 3.14 \)[/tex] from our earlier calculation:
[tex]\[ V = 3.14 \cdot 80 \][/tex]
[tex]\[ V \approx 251.2 \][/tex]
The volume of cylinder B is approximately 251.2 cubic inches. This matches the given choice of 251.2 cubic inches.
[tex]\[ V = k \cdot r^2 \cdot h \][/tex]
1. Determine the constant [tex]\( k \)[/tex] using Cylinder A:
- Cylinder A has a volume ([tex]\( V \)[/tex]) of 254.34 cubic inches, a radius ([tex]\( r \)[/tex]) of 3 inches, and a height ([tex]\( h \)[/tex]) of 9 inches.
- Substitute these values into the formula to solve for [tex]\( k \)[/tex]:
[tex]\[ 254.34 = k \cdot 3^2 \cdot 9 \][/tex]
[tex]\[ 254.34 = k \cdot 9 \cdot 9 \][/tex]
[tex]\[ 254.34 = k \cdot 81 \][/tex]
- Divide both sides by 81 to find [tex]\( k \)[/tex]:
[tex]\[ k = \frac{254.34}{81} \][/tex]
2. Calculate the volume of Cylinder B:
- Cylinder B has a radius ([tex]\( r \)[/tex]) of 4 inches and a height ([tex]\( h \)[/tex]) of 5 inches.
- Use the same formula to calculate the volume ([tex]\( V \)[/tex]) for Cylinder B:
[tex]\[ V = k \cdot 4^2 \cdot 5 \][/tex]
[tex]\[ V = k \cdot 16 \cdot 5 \][/tex]
[tex]\[ V = k \cdot 80 \][/tex]
3. Substitute the value of [tex]\( k \)[/tex] from the first step into the formula for Cylinder B:
- Given that [tex]\( k \approx 3.14 \)[/tex] from our earlier calculation:
[tex]\[ V = 3.14 \cdot 80 \][/tex]
[tex]\[ V \approx 251.2 \][/tex]
The volume of cylinder B is approximately 251.2 cubic inches. This matches the given choice of 251.2 cubic inches.
Thank you for reading the article The volume of a cylinder varies jointly with the square of its radius and with its height tex V k r 2 h tex Cylinder. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
- You are operating a recreational vessel less than 39 4 feet long on federally controlled waters Which of the following is a legal sound device
- Which step should a food worker complete to prevent cross contact when preparing and serving an allergen free meal A Clean and sanitize all surfaces
- For one month Siera calculated her hometown s average high temperature in degrees Fahrenheit She wants to convert that temperature from degrees Fahrenheit to degrees
Rewritten by : Jeany
