The area of the vase lies between the area [tex]135\ cm^2[/tex] and [tex]155\ cm^2[/tex] will be [tex]153.86\ cm^2[/tex].
As we know that the area of the circle is given by the formula
[tex]A=\pi r^2[/tex]
So now from the question, we will find the radius for both the given areas.
Radius for the first area
[tex]r=\dfrac{A}{\pi} =\dfrac{135}{\pi} =6.56\ cm[/tex]
Radius for the second area
[tex]r=\dfrac{A}{\pi} =\dfrac{155}{\pi} =7.03\ cm[/tex]
Now we can see the range of the radius lies
[tex]6.56\leq r\leq 7.03[/tex]
The radius must be r=7 cm lie between two quantities.
Then the area at r= 7cm will be
[tex]A=\pi r^2[/tex]
[tex]A=\pi\times 7^2=153.86\ cm^2[/tex]
Thus the area for the vase will be [tex]A=153.86\ cm^2[/tex] ar radius r= 7 cm
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