Question

directions: find the area and circumference of each circle below.
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1. the radius of circle a is three feet less than twice the diameter of circle b. if the sum of the diameters of both circles is 49 feet, find the area and circumference of circle a.

Explanation:

Step1: Circle 2: Calculate Circumference

Use $C=2\pi r$, $r=7$ m
$C=2\pi(7)=14\pi\approx43.98$ m

Step2: Circle 2: Calculate Area

Use $A=\pi r^2$, $r=7$ m
$A=\pi(7)^2=49\pi\approx153.94$ m²

Step3: Circle3: Find radius first

$r=\frac{30}{2}=15$ ft

Step4: Circle3: Calculate Circumference

$C=2\pi(15)=30\pi\approx94.25$ ft

Step5: Circle3: Calculate Area

$A=\pi(15)^2=225\pi\approx706.86$ ft²

Step6: Circle4: Calculate Circumference

Use $C=2\pi r$, $r=10.2$ in
$C=2\pi(10.2)=20.4\pi\approx64.09$ in

Step7: Circle4: Calculate Area

$A=\pi(10.2)^2=104.04\pi\approx326.85$ in²

Step8: Circle5: Find radius first

$r=\frac{9}{2}=4.5$ mm

Step9: Circle5: Calculate Circumference

$C=2\pi(4.5)=9\pi\approx28.27$ mm

Step10: Circle5: Calculate Area

$A=\pi(4.5)^2=20.25\pi\approx63.62$ mm²

Step11: Circle6: Define variables

Let $d_B$ = diameter of Circle B, diameter of Circle A $d_A=2r_A=2(2d_B-3)=4d_B-6$

Step12: Solve for $d_B$

Sum: $d_A+d_B=49$
$4d_B-6+d_B=49$
$5d_B=55$
$d_B=11$ ft

Step13: Find $r_A$

$r_A=2(11)-3=19$ ft

Step14: Circle6: Calculate Circumference

$C=2\pi(19)=38\pi\approx119.38$ ft

Step15: Circle6: Calculate Area

$A=\pi(19)^2=361\pi\approx1134.11$ ft²

Answer:

1. Circumference: $14\pi$ m (≈43.98 m), Area: $49\pi$ m² (≈153.94 m²)
2. Circumference: $30\pi$ ft (≈94.25 ft), Area: $225\pi$ ft² (≈706.86 ft²)
3. Circumference: $20.4\pi$ in (≈64.09 in), Area: $104.04\pi$ in² (≈326.85 in²)
4. Circumference: $9\pi$ mm (≈28.27 mm), Area: $20.25\pi$ mm² (≈63.62 mm²)
5. Circumference of Circle A: $38\pi$ ft (≈119.38 ft), Area of Circle A: $361\pi$ ft² (≈1134.11 ft²)