we know that
[the area of a original circle]=pi*r²
[the circumference of a original circle]=2*pi*r
[the ratio of the area to the circumference]=[pi*r²]/[2*pi*r]---> r/2
so
r/2=14-------> r=14*2------> r=28 units
Part a) find the circumference of the circle with twice the radius of the given circle
r=2*28 units
[the circumference of a new circle]=2*pi*2*r-----> 2*[2*pi*r]
so
[the circumference of a new circle]=2*[the circumference of a original circle]
[the circumference of a new circle]=2*[2*pi*28]--> 2*56*pi---> 112*pi units
the circumference of a new circle is two times greater than the circumference of a original circle
Part b) find the area of the circle with twice the radius of the given circle
[the area of a original circle]=pi*r²
[the area of a new circle]=pi*(2*r)²----> 4*[pi*r²]
so
[the area of a new circle]=4*[the area of a original circle]
[the area of a new circle]=4*pi*28²-----> 4*784*pi ----> 3136*pi units²
the area of a new circle is four times greater than the area of a original circle
the answer is
the circumference of a new circle is 112*pi units
the area of a new circle is 3136*pi units²
