Question

Explain it clearly and easy to understand. Show step-by-step. (In this

Circles
ANSWERED
asked 2021-08-09
Explain it clearly and easy to understand. Show step-by-step. (In this in case, \(\displaystyle\pi={3.1416}\)) Round the answer to the nearest tenth.
There are two circles. The diameter of the first is 12 in. and the area of the second is \(\displaystyle{2}{\frac{{{1}}}{{{4}}}}\) times the area of the first. What is the diameter of the second circle?

Answers (1)

2021-08-10

Step 1
Let d and \(\displaystyle{A}_{{{1}}}\) be the diameter and area of first circle and D and \(\displaystyle{A}_{{{2}}}\) be diameter and area of second circle.
Then , according to given condition,
\(\displaystyle{d}={12}\)
and
\(\displaystyle{A}_{{{2}}}={2}{\frac{{{1}}}{{{4}}}}{A}_{{{1}}}\)
\(\displaystyle{A}_{{{2}}}={\frac{{{9}}}{{{4}}}}{A}_{{{1}}}\)
We know that area of circle is \(\pi r^2\) , that is \(\pi \frac{dr^2}{2}\)
Step 2
Therefore, \(\displaystyle{A}_{{{2}}}={\frac{{{9}}}{{{4}}}}{A}_{{{1}}}\)
\(\displaystyle\pi{\left({\frac{{{D}}}{{{2}}}}\right)}^{{{2}}}={\frac{{{9}}}{{{4}}}}\pi{\left({\frac{{{d}}}{{{2}}}}\right)}^{{{2}}}\)
\(\displaystyle{D}^{{{2}}}={\frac{{{9}}}{{{4}}}}{d}^{{{2}}}\)
\(\displaystyle{D}={\frac{{{3}}}{{{2}}}}{d}\)
\(\displaystyle{D}={\frac{{{3}}}{{{2}}}}{\left({12}\right)}={24}\) in.
Step 3
Answer: Diameter of second circle is 24 in.

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours

Relevant Questions

asked 2021-05-05
If John, Trey, and Miles want to know how’ | many two-letter secret codes there are that don't have a repeated letter. For example, they want to : count BA and AB, but they don't want to count“ doubles such as ZZ or XX. Jobn says there are 26 + 25 because you don’t want to use the same letter twice; that’s why the second number is 25.
‘Trey says he thinks it should be times, not plus: 26-25, Miles says the number is 26-26 ~ 26 because you need to take away the double letters. Discuss the boys’ ideas, Which answers are correct, which are not, and why? Explain your answers clearly and thoroughly, drawing ‘on this section’s definition of multiptication.. -
asked 2021-06-10
Here’s an interesting challenge you can give to a friend. Hold a $1 (or larger!) bill by an upper corner. Have a friend prepare to pinch a lower corner, putting her fingers near but not touching the bill. Tell her to try to catch the bill when you drop it by simply closing her fingers. This seems like it should be easy, but it’s not. After she sees that you have released the bill, it will take her about 0.25 s to react and close her fingers-which is not fast enough to catch the bill. How much time does it take for the bill to fall beyond her grasp? The length of a bill is 16 cm.
asked 2021-08-06
In your own words, discuss how the diameter and circumference of all circles-small or large-are related. What is a hands-on way to see this relationship? If a circle has diameter D centimeters and circumference C centimeters, then what is an equation that relates D and C? Explain in detail why your equations holds for all circles, no matter what size.
asked 2021-02-12

Use the definition of Laplace Transforms to find \(L\left\{f(t)\right\}\)
\(f(t)=\begin{cases}-1 & 0\leq t <1\\1 & t\geq 1\end{cases}\)
Then rewrite f(t) as a sum of step functions, \(u_c(t)\), and show that by taking Laplace transforms, this yields the same answer as your direct computation.

...