Answer:
The true statements are:
C. If the metal has a radius of 2.5 inches then it has an area of 19.625 in.²
D. If the metal has a diameter of 3 inches and it has a circumference of 9.42 inches.
E. If the metal has a circumference of four pi inches then it has an area of four pi square inches
Step-by-step explanation:
Let us revise the rule of circumference and area of a circle
- The formula of the circumference of a circle is <em>C = π d</em>, where d is the diameter of the circle OR <em>C = 2πr</em>, where r is the radius of the circle
- The formula of the area of a circle is <em>A = πr²</em>
- The radius of a circle is equal to half its diameter
A.
∵ The metal has a circumference of 7π inches
∵ C = 2πr
- Equate πd by 7π
∴ πd = 7π
- Divide both sides by π
∴ d = 7 inches not 3.5 inches
∴ A is not true
B.
∵ The metal has a circumference of 3π inches
∵ C = 2πr
- Equate 2πr by 3π
∴ 2πr = 3π
- Divide both sides by π
∴ 2r = 3
- Divide both sides by 2
∴ r = 1.5 inches
∵ A = πr²
∴ A = π(1.5)²
∴ A = 2.25π inches² not 9π inches²
∴ B is not true
C.
∵ The metal has a radius of 2.5 inches
∴ r = 2.5
∵ A = πr²
∵ π = 3.14
∴ A = 3.14(2.5)²
∴ A = 19.625 inches²
∴ If the metal has a radius of 2.5 inches, then its area is 19.625 in.²
∴ C is true
D.
∵ The metal has a diameter of 3 inches
∴ d = 3
∵ C = πd
∵ π = 3.14
∴ C = 3.14(3)
∴ C = 9.42 inches
∴ If the metal has a diameter of 3 inches, then its circumference
is 9.42 inches
∴ D is true
E.
∵ The metal has a circumference of 4π inches
∵ C = 2πr
- Equate 2πr by 4π
∴ 2πr = 4π
- Divide both sides by 2π
∴ r = 2
- Now you can find the area
∵ A = πr²
∴ A = π(2)²
∴ A = 4π
∴ If the metal has a circumference of 4π inches, then its area
is 4π inches²
∴ E is true
The true statements are:
C. If the metal has a radius of 2.5 inches then it has an area of 19.625 in.²
D. If the metal has a diameter of 3 inches and it has a circumference of 9.42 inches.
E. If the metal has a circumference of four pi inches then it has an area of four pi square inches
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