Welcome to Westonci.ca, where your questions are met with accurate answers from a community of experts and enthusiasts. Our Q&A platform offers a seamless experience for finding reliable answers from experts in various disciplines. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To determine the factor by which the dimensions of cylinder [tex]\(A\)[/tex] are multiplied to produce the corresponding dimensions of cylinder [tex]\(B\)[/tex], we need to understand and find the radii of the bases of both cylinders.
1. Find the radius of cylinder [tex]\(A\)[/tex]:
- We know the circumference of the base of cylinder [tex]\(A\)[/tex] is [tex]\(4\pi\)[/tex] units.
- The formula for the circumference [tex]\(C\)[/tex] of a circle is given by:
[tex]\[ C = 2\pi r \][/tex]
- Solving for the radius [tex]\(r\)[/tex]:
[tex]\[ 4\pi = 2\pi r \implies r = \frac{4\pi}{2\pi} = 2 \text{ units} \][/tex]
Thus, the radius of the base of cylinder [tex]\(A\)[/tex] is [tex]\(2\)[/tex] units.
2. Find the radius of cylinder [tex]\(B\)[/tex]:
- We know the area of the base of cylinder [tex]\(B\)[/tex] is [tex]\(9\pi\)[/tex] square units.
- The formula for the area [tex]\(A\)[/tex] of a circle is given by:
[tex]\[ A = \pi r^2 \][/tex]
- Solving for the radius [tex]\(r\)[/tex]:
[tex]\[ 9\pi = \pi r^2 \implies r^2 = 9 \implies r = \sqrt{9} = 3 \text{ units} \][/tex]
Thus, the radius of the base of cylinder [tex]\(B\)[/tex] is [tex]\(3\)[/tex] units.
3. Calculate the multiplication factor:
- To determine the factor by which the dimensions of cylinder [tex]\(A\)[/tex] are multiplied to produce cylinder [tex]\(B\)[/tex], we take the ratio of the radii of the two cylinders.
[tex]\[ \text{Factor} = \frac{\text{Radius of } B}{\text{Radius of } A} = \frac{3}{2} \][/tex]
Therefore, the dimensions of cylinder [tex]\(A\)[/tex] are multiplied by the factor [tex]\(\frac{3}{2}\)[/tex] to produce the dimensions of cylinder [tex]\(B\)[/tex].
So, the answer is [tex]\(\boxed{\frac{3}{2}}\)[/tex].
1. Find the radius of cylinder [tex]\(A\)[/tex]:
- We know the circumference of the base of cylinder [tex]\(A\)[/tex] is [tex]\(4\pi\)[/tex] units.
- The formula for the circumference [tex]\(C\)[/tex] of a circle is given by:
[tex]\[ C = 2\pi r \][/tex]
- Solving for the radius [tex]\(r\)[/tex]:
[tex]\[ 4\pi = 2\pi r \implies r = \frac{4\pi}{2\pi} = 2 \text{ units} \][/tex]
Thus, the radius of the base of cylinder [tex]\(A\)[/tex] is [tex]\(2\)[/tex] units.
2. Find the radius of cylinder [tex]\(B\)[/tex]:
- We know the area of the base of cylinder [tex]\(B\)[/tex] is [tex]\(9\pi\)[/tex] square units.
- The formula for the area [tex]\(A\)[/tex] of a circle is given by:
[tex]\[ A = \pi r^2 \][/tex]
- Solving for the radius [tex]\(r\)[/tex]:
[tex]\[ 9\pi = \pi r^2 \implies r^2 = 9 \implies r = \sqrt{9} = 3 \text{ units} \][/tex]
Thus, the radius of the base of cylinder [tex]\(B\)[/tex] is [tex]\(3\)[/tex] units.
3. Calculate the multiplication factor:
- To determine the factor by which the dimensions of cylinder [tex]\(A\)[/tex] are multiplied to produce cylinder [tex]\(B\)[/tex], we take the ratio of the radii of the two cylinders.
[tex]\[ \text{Factor} = \frac{\text{Radius of } B}{\text{Radius of } A} = \frac{3}{2} \][/tex]
Therefore, the dimensions of cylinder [tex]\(A\)[/tex] are multiplied by the factor [tex]\(\frac{3}{2}\)[/tex] to produce the dimensions of cylinder [tex]\(B\)[/tex].
So, the answer is [tex]\(\boxed{\frac{3}{2}}\)[/tex].
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Westonci.ca is here to provide the answers you seek. Return often for more expert solutions.