HELP!!! Please help me with this math problem.
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Answer:
Part 1: r = √(A/π)
Part 2: 4.15 cm
Step-by-step explanation:
Part 1
The area of a circle is given by;
Area = π r²
A = πr²
dividing both sides by π
r² = A/π
Find the square root on both sides of the equation
r = √(A/π)
Part 2
where π = 22/7 and
r is the radius os the circle
Area = 54 cm²
πr² = 54
22/7 × r² = 54
Multiplying both sides of the equation by 7/22
7/22 × 22/7 ×r² = 54 ×7/22
r² = 189/11
= 17.181818..
r = √17.181818
= 4.145
Answer to the nearest hundredth = 4.15 cm
Answer:
i) [tex]r= \sqrt{\frac{A}{\pi} }[/tex]
ii) [tex]r=4.15[/tex] centimeters
Step-by-step explanation:
The area of a circle is given by;
[tex]A=\pi r^2[/tex]
We want to solve for r.
Divide both sides by [tex]\pi[/tex].
This implies that;
[tex]\frac{A}{\pi} =r^2[/tex]
Take positive square root of both sides;
[tex]\Rightarrow r= \sqrt{\frac{A}{\pi} }[/tex]
When we substitute;
[tex]A=54cm^2[/tex]
and
[tex]\pi=\frac{22}{7}[/tex]
We obtain;
[tex]r=\sqrt{\frac{54}{\frac{22}{7} }}[/tex]
[tex]r=\sqrt{54\times \frac{7}{22}}[/tex]
[tex]r=\sqrt{17.18}[/tex]
[tex]r=4.15[/tex] centimeters