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 π.

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area of a circle is \(A = \pi r^{2}\), where \(r\) is the radius of the circle.

Step2: Calculate the area for each circle

• For the circle with \(r = 6\space cm\):

Substitute \(r = 6\) and \(\pi=3.14\) into the formula \(A=\pi r^{2}\).
\(A = 3.14\times6^{2}=3.14\times36 = 113.04\space cm^{2}\)

• For the circle with \(r = 7\space cm\):

Substitute \(r = 7\) and \(\pi = 3.14\) into the formula \(A=\pi r^{2}\).
\(A=3.14\times7^{2}=3.14\times49 = 153.86\space cm^{2}\)

• For the circle with \(r = 8\space cm\):

Substitute \(r = 8\) and \(\pi=3.14\) into the formula \(A=\pi r^{2}\).
\(A=3.14\times8^{2}=3.14\times64 = 200.96\space cm^{2}\)

Answer:

The circle with radius \(7\space cm\) (the second option)