Question

lesson 6 - session 3
finding the area of a circle a = πr² = 1/2d·r

find the radius of each circle. show your work.

1. 12 in
2. 26 cm

r = 6 in
r = 13 cm

find the area of each circle. write your answer using π.

1. 20 yd
2. 8 ft

a = 100π yd²

1. 4 mm
2. 14 in

Explanation:

Step1: Recall radius - diameter relationship

The radius $r$ of a circle is half of its diameter $d$, i.e., $r=\frac{d}{2}$. The area formula of a circle is $A = \pi r^{2}$.

Step2: Solve for circle 4

Given the diameter $d = 8$ ft. Using $r=\frac{d}{2}$, we have $r=\frac{8}{2}=4$ ft. Then, using the area formula $A=\pi r^{2}$, we substitute $r = 4$ into it: $A=\pi\times(4)^{2}=16\pi$ ft².

Step3: Solve for circle 5

Given the radius $r = 4$ mm. Using the area formula $A=\pi r^{2}$, we substitute $r = 4$ into it: $A=\pi\times(4)^{2}=16\pi$ mm².

Step4: Solve for circle 6

Given the diameter $d = 14$ in. Using $r=\frac{d}{2}$, we have $r=\frac{14}{2}=7$ in. Then, using the area formula $A=\pi r^{2}$, we substitute $r = 7$ into it: $A=\pi\times(7)^{2}=49\pi$ in².

Answer:

1. $16\pi$ ft²
2. $16\pi$ mm²
3. $49\pi$ in²