Question

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 pi.

A.23 in.
B.24 in.
C.25 in.
D.26 in.

Answer 1

we know that

the area of a circle is equal to

$A=\pi r^{2}$

where

r is the radius of the circle

Step 1

Find the radius for $A=1,650\ in^{2}$

$A=\pi r^{2}$

Solve for r

$r=\sqrt{\frac{A}{\pi}}$

substitute the value of area

$r=\sqrt{\frac{1,650}{3.14}}=22.92\ in$

Step 2

Find the radius for $A=1,700\ in^{2}$

$A=\pi r^{2}$

Solve for r

$r=\sqrt{\frac{A}{\pi}}$

substitute the value of area

$r=\sqrt{\frac{1,700}{3.14}}=23.27\ in$

therefore

the radius r

$22.92\ in \leq r \leq 23.27\ in$

the answer is the option A

$23\ in$

Answer 2

You can use formula for area of square to get an equation in terms of radius and some constants. Then use some operations necessary to get the value of radius.

The length of the radius of the given circle is approximately given by:

Option A: 23 inches.

What is the area of a circle?

The area of a circle with radius r units is given by:

$Area = \pi \times r^2 \: \rm \: unit^2$

Using that definition and the fact that the area of the considered circle lies between  1,650 and 1,700 square inches

$1650 < Area < 1700\\1650 < \pi \times r^2 < 1700\\\\\text{Dividing by } \pi \text{\: on all three sides, we get:}\\\\\dfrac{1650}{3.14} < r^2 < \dfrac{1700}{3.14}\\\\525.478 < r^2 < 541.401\\\\\text{Taking positive roots on all sides( since the radius is a non negative quantity)}\\\\\sqrt{525.478} < r < \sqrt{541.401}\\22.92 < r < 23.26\\\\Thus,\\r \approx 23 \: \rm \: inches$

Thus,

the radius of the circle is approximately 23 inches.

Thus,

The length of the radius of the given circle is approximately given by:

Option A: 23 inches.

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