Question

48 PTS!!!!!!A circular disc has an area that measures between 1,650 and 1,700 square inches.

Answer 1

Answer:

23 in

Step-by-step explanation:

The area of a circle is given by the formula: πr²

So we know that the area of this circle is between 1650 and 1700 square inches and we need to know which could be the length of its radius.

Writing this in an inequality we would have

1650 < πr² < 1700

Since we want to know what r might be, we are going to solve for r:

1650 < πr² < 1700

1650/π < r² < 1700/π

1650/3.14 < r² <1700/3.14

525.47 < r² < 541.40

√525.47 < √r² < √541.40

22.92 < r < 23.26

Thus, the radius is between 22.92 inches and 23.26 inches.

Thus, from our options, we can see that the only one possible between this range would be 23 in  

Answer 2

Answer:

A. 23 in.

Step-by-step explanation:

Let r represent the radius of the circular disc.

We have been given that a circular disc has an area that measures between 1,650 and 1,700 square inches.

We will use area of circle formula to solve our given problem.

$\text{Area of circle}=\pi r^2$, where r represents radius of circle.

Since the area of given disc is between 1650 and 1700 square inches, so we can set an inequality as:

$1650\text{ inch}^2$

$1650\text{ inch}^2$

Dividing our inequality by 3.14 we will get,

$\frac{1650\text{ inch}^2}{3.14}$

$525.477707006\text{ inch}^2$

Upon taking square root we will get,

$\sqrt{525.477707006\text{ inch}^2}$

$22.9233\text{ inch}$

Since 23 is between 22.9233 and 23.268031156, therefore, the length of radius of the given disc could be 23 inches and option A is the correct choice.