Question

question 23 points 3
werry bought a circular shaped toy, the area of the toy is 804.25 sq.cm. find the toys diameter and radius
4 cm
3 cm
12 cm
16 cm

Explanation:

Step1: Recall the formula for the area of a circle

The area formula of a circle is \(A = \pi r^{2}\), where \(A\) is the area and \(r\) is the radius. Given \(A = 804.25\space cm^{2}\) and taking \(\pi=\frac{22}{7}\) (a common approximation).

Step2: Solve for the radius \(r\)

We have \(804.25=\frac{22}{7}\times r^{2}\). First, solve for \(r^{2}\): \(r^{2}=\frac{804.25\times7}{22}\).
\(r^{2}=\frac{5629.75}{22}=255.9\approx256\). Then, take the square - root: \(r = \sqrt{256}=16\space cm\).

Step3: Calculate the diameter \(d\)

Since the diameter \(d = 2r\), substituting \(r = 16\space cm\), we get \(d=2\times16 = 32\space cm\). But wait, there is a mistake. Let's use \(\pi = 3.14\) (another common approximation).
If \(A=\pi r^{2}\), then \(r^{2}=\frac{A}{\pi}\). Substituting \(A = 804.25\) and \(\pi=3.14\), we have \(r^{2}=\frac{804.25}{3.14}=256.13\approx256\). \(r=\sqrt{256} = 16\space cm\).

Answer:

The radius of the circular - shaped toy is \(16\space cm\) and the diameter is \(32\space cm\).