Answer:
17) 4 inches
18) 14 yards
19) 162 yards
20) 30 yards
Step-by-step explanation:
To find the diameter of each circle, we'll use the following formulas:
Area of a circle: [tex]\sf \textsf{Area} = \pi r^2 [/tex]
Circumference of a circle: [tex]\sf \textsf{Circumference} = 2 \pi r [/tex]
Given the values provided, we'll use the information to solve for the radius ([tex]\sf r [/tex]) first, and then calculate the diameter ([tex]\sf d [/tex]).
17) Area = [tex]\sf 4 \pi [/tex] in²
[tex]\sf \textsf{Area} = \pi r^2 [/tex]
[tex]\sf 4 \pi = \pi r^2 [/tex]
Divide both sides by [tex]\sf \pi [/tex]:
[tex]\sf r^2 = 4 [/tex]
Take the square root of both sides:
[tex]\sf r = \sqrt{4} [/tex]
[tex]\sf r = 2 [/tex]
Since diameter [tex]\sf d = 2r [/tex]:
[tex]\sf d = 2 \times 2 = 4 \textsf{ inches} [/tex]
19) Circumference = [tex]\sf 162 \pi [/tex] yd
[tex]\sf \textsf{Circumference} = 2 \pi r [/tex]
[tex]\sf 162 \pi = 2 \pi r [/tex]
Divide both sides by [tex]\sf 2 \pi [/tex]:
[tex]\sf r = \dfrac{162 \pi}{2 \pi} [/tex]
[tex]\sf r = 81 \textsf{ yards} [/tex]
Since diameter [tex]\sf d = 2r [/tex]:
[tex]\sf d = 2 \times 81 = 162 \textsf{ yards} [/tex]
18) Area = [tex]\sf 49 \pi [/tex] yd²
[tex]\sf \textsf{Area} = \pi r^2 [/tex]
[tex]\sf 49 \pi = \pi r^2 [/tex]
Divide both sides by [tex]\sf \pi [/tex]:
[tex]\sf r^2 = 49 [/tex]
Take the square root of both sides:
[tex]\sf r = \sqrt{49} [/tex]
[tex]\sf r = 7 \textsf{ yards} [/tex]
Since diameter [tex]\sf d = 2r [/tex]:
[tex]\sf d = 2 \times 7 = 14 \textsf{ yards} [/tex]
20) Circumference = [tex]\sf 30 \pi [/tex] yd
[tex]\sf \textsf{Circumference} = 2 \pi r [/tex]
[tex]\sf 30 \pi = 2 \pi r [/tex]
Divide both sides by [tex]\sf 2 \pi [/tex]:
[tex]\sf r = \dfrac{30 \pi}{2 \pi} [/tex]
[tex]\sf r = 15 \textsf{ yards} [/tex]
Since diameter [tex]\sf d = 2r [/tex]:
[tex]\sf d = 2 \times 15 = 30 \textsf{ yards} [/tex]
So, the diameters of the given circles are:
17) 4 inches
18) 14 yards
19) 162 yards
20) 30 yards
