Question

Liliana is making a vase with a circular base. She wants the area of the base to be between 135 cm2 and 155 cm2. Which circle could represent the base of the vase? Use 3. 14 for Pi.

Answer 1

The area of the vase lies between the area $135\ cm^2$ and $155\ cm^2$ will be $153.86\ cm^2$.

What will be the area?

As we know that the area of the circle is given by the formula

$A=\pi r^2$

So now from the question, we will find the radius for both the given areas.

Radius for the first area

$r=\dfrac{A}{\pi} =\dfrac{135}{\pi} =6.56\ cm$

Radius for the second area

$r=\dfrac{A}{\pi} =\dfrac{155}{\pi} =7.03\ cm$

Now we can see the range of the radius lies

$6.56\leq r\leq 7.03$

The radius must be r=7 cm lie between two quantities.

Then the area at r= 7cm will be

$A=\pi r^2$

$A=\pi\times 7^2=153.86\ cm^2$

Thus the area for the vase will be $A=153.86\ cm^2$ ar radius r= 7 cm

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