What is the diameter of the circle, and what is the area of a circle with a radius of 12m?
Understand the Problem
The question asks to first find the diameter of a circle with a given radius of 12m, then find the area of the same circle.
Answer
Diameter: $24m$ Area: $452.16 m^2$
Answer for screen readers
Diameter: $24m$ Area: $452.16 m^2$
Steps to Solve
- Find the diameter
The diameter of a circle is twice the radius. Given the radius $r = 12m$, we can find the diameter $d$ using the formula $d = 2r$
- Calculate the diameter
Substitute the given radius into the formula:
$d = 2 \times 12m = 24m$
- Find the area
The area of a circle is given by the formula $A = \pi r^2$
- Calculate the area
Substitute the given radius $r = 12m$ into the formula, using $\pi \approx 3.14$:
$A = \pi (12m)^2 = 3.14 \times 144 m^2 = 452.16 m^2$
Diameter: $24m$ Area: $452.16 m^2$
More Information
The area of the circle is approximately $452.16 m^2$, calculated using $\pi \approx 3.14$. If a more precise value of $\pi$ is used, the area will be slightly different.
Tips
A common mistake is to confuse the radius and the diameter. Remember the diameter is twice the radius. Also, ensure correct units are used, especially when calculating the area (which should be in square meters in this case).
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