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

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)


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,
We know that area of circle is \(\pi r^2\) , that is \(\pi \frac{dr^2}{2}\)
Step 2
Therefore, \(\displaystyle{A}_{{{2}}}={\frac{{{9}}}{{{4}}}}{A}_{{{1}}}\)
\(\displaystyle{D}={\frac{{{3}}}{{{2}}}}{\left({12}\right)}={24}\) in.
Step 3
Answer: Diameter of second circle is 24 in.

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