Answer with Step-by-step explanation:
a.If the circle has circumference of [tex]6\pi[/tex] in,then it has a diameter of 3 in.
Circumference of circle=[tex]6\pi[/tex]in
We know that
Circumference of circle=[tex]2\pi r[/tex]
Using the formula
[tex]6\pi=2\pi r[/tex]
[tex]r=\frac{6\pi}{2\pi}=3[/tex]in
Diameter of circle=[tex]2\times 3=6[/tex]in
It is false.
b.f the circle has diameter of 2 inches,then it has a circumference of 6.28 in.
Diameter,d=2 in
Circumference of circle=[tex]\pi d=3.14 \times 2=6.28[/tex]in
It is true.
c.If the circle has a circumference of [tex]2\pi[/tex]in then it has an area [tex]\pi[/tex] square inches.
Circumference=[tex]2\pi[/tex]in
[tex]2\pi r=2\pi[/tex]
[tex]r=\frac{2\pi}{2\pi}=1[/tex]in
Area of circle=[tex]\pi r^2=\pi(1)^2=\pi in^2[/tex]
It is true.
d.If the circle has a circumference of [tex]\pi[/tex]in then it has an area [tex]0.5\pi[/tex] square inches.
Circumference=[tex]\pi[/tex]in
[tex]2\pi r=\pi[/tex]
[tex]r=\frac{\pi}{2\pi}=\frac{1}{2}in[/tex]
Area of circle=[tex]\pi(\frac{1}{2})^2=0.25\pi in^2[/tex]
It is not true.
e.If the circle has a radius of 1.5 inches,then it has an area of 7.065 square inches.
Radius,r=1.5 in
Area of circle=[tex]3.14\times (1.5)^2=7.065in^2[/tex]
It is true.
