Answer:
r = 1.71 km
Step-by-step explanation:
We are given that a quarter of a circle has a perimeter of 10.71 kilometers. We want to know what the radius is of this quarter circle.
Recall that the perimeter of a full circle is [tex]2\pi r[/tex], where r is the radius of the circle. But, since we have the quarter of the circle, the perimeter of the quarter circle is [tex]\frac{2\pi r}{4}[/tex].
This means that [tex]\frac{2\pi r}{4} = 10.71[/tex]
So, multiply both sides by 4.
We get:
[tex]2\pi r = 42.84[/tex]
Now, divide both sides by 2.
[tex]\pi r = 21.42[/tex]
Since we want to use 3.14 for pi, we now have:
3.14r = 21.42
Divide both sides by 3.14 to get:
6.82 = r (rounded to the nearest hundredth).
But remember this r value is for the full circle, not the quarter circle. So, divide 6.82 by 4.
In that case, the quarter circle's radius is 6.82 / 4 = 1.71 km.
Answer:
→ 1.71 km
Step-by-step explanation:
Given :
We have to find :
Solution :
We know that perimeter that is circumference of a circle is given by :
But according to question we are given the perimeter of quarter circle which means :
Now ,
[tex]\sf{\longmapsto\;\;\;\dfrac{2\pi\;r}{4} =10.71}[/tex]
Multiplying both sides by 4 ;
[tex]\sf{\longmapsto\;\;\;\dfrac{2\pi\;r}{\cancel{4}} \times\cancel{4}=10.71\times4}[/tex]
We get ,
[tex]\sf{\longmapsto\;\;\;2\pi\;r =42.84}[/tex]
[tex]\sf{\longmapsto\;\;\; 2\times3,14r=42,84}[/tex]
[tex]\sf{\longmapsto\;\;\;6.28r=42.84}[/tex]
[tex]\sf{\longmapsto\;\;\;r =\dfrac{42.84}{6.28} }[/tex]
We get :
[tex]\sf{\longmapsto\;\;\;r=6.82 \:km}[/tex]
But we have to find the radius of quarter circle , therefore dividing the radius with 4 :
>>> Therefore , radius of quarter circle is "1.71 kilometres".
