A circular disc has an area that measures between 1,650 and 1,700 square inches. What could be the length of its radius? Use 3.14 for pie

Respuesta :

Answer:

According to this description the area [tex]A[/tex] of the disc is:

[tex]1650in^{2}<A<1700in^{2}[/tex]

On the other hand, the area of a circumference is given by the following equation:

[tex]A=\pi r^{2}[/tex]   (1)

Where [tex]r[/tex] is the radius.

If we want to know the possible lengths of [tex]r[/tex] for the circular disc, we will have to apply equation (1) for both areas:

For [tex]A=1650in^{2}[/tex]:

[tex]1650in^{2}=3.14 r^{2}[/tex]  

[tex]r=\sqrt{\frac{1650in^{2}}{3.14}}[/tex]  

[tex]r=22.91 inches[/tex]  

For [tex]A=1700in^{2}[/tex]:

[tex]1700in^{2}=3.14 r^{2}[/tex]  

[tex]r=\sqrt{\frac{1700in^{2}}{3.14}}[/tex]  

[tex]r=23.26 inches[/tex]  

Therefore the radius could be 22.91 inches or 23.26 inches

Answer:

22.92 inches ≤ r ≤ 23.27 inches

Step-by-step explanation:

We are given that the area of a circular disk has an area measuring between 1650 and 1700 square inches and we are to find the possible length of the its radius.

We know that  the area of a circle is equal is given by [tex]\pi r^2[/tex].

Finding radius for 1650:

[tex]r=\sqrt{\frac{1,650}{3.14}}=22.92\ in[/tex]

Finding radius for 1700:

[tex]r=\sqrt{\frac{1,700}{3.14}}=23.27\ inches[/tex]

Therefore, 22.92 inches ≤ r ≤ 23.27 inches.