Finding the Radius of a Circle Given Its Area

To find the radius of a circle given its area, you can use the formula for the area of a circle: A pi r^2

A is the area of the circle. r is the radius.

Correct Solution for Area 2464 cm2

Given that the area

A 2464 , text{cm}^2,

you can rearrange the formula to solve for the radius r: r^2 frac{A}{pi}

Substituting the area into the equation:

r^2 frac{2464}{pi}

Using pi approx frac{22}{7} (a common and fairly accurate approximation for (pi)):

r^2 approx frac{2464 times 7}{22} frac{17248}{22} approx 784

Now take the square root to find r:

r approx sqrt{784} approx 28 , text{cm}

Thus, the radius of the circle is approximately 28 cm.

Alternative Approximations for (pi)

Many people use (pi approx frac{22}{7}) as an approximation, but a more accurate approximation for (pi) is (frac{355}{113}).

If you use a calculator with (pi) and round at the end:

r sqrt{frac{2464}{3.141592653589793}} approx 28.005634425180591 approx 28 , text{cm}

Therefore, the radius of the circle is approximately 28 cm.

Significance of Units in Area Calculation

It is essential to use the correct units for area, which are square units (e.g., cm2, m2).

Given the area of the circle is 2464 cm2, the radius can be calculated as follows:

2464 pi r^2

Using (pi approx frac{22}{7}):

r^2 frac{2464 times 7}{22} frac{17248}{22} approx 784

So, the radius r approx sqrt{784} 28 , text{cm}.

Therefore, the radius of the given circle is 28 cm.