How to find area using diameter?
Understand the Problem
The question is asking how to calculate the area of a circle using its diameter. The area can be found by using the formula: Area = π * (radius)^2, and since the radius is half the diameter, the formula can be rewritten in terms of diameter as Area = (π/4) * (diameter)^2.
Answer
The area of a circle is given by the formula $A = \frac{π}{4} d^2$.
Answer for screen readers
The area of a circle in terms of its diameter is given by the formula: $$ A = \frac{π}{4} d^2 $$
Steps to Solve
- Identify the relationship between diameter and radius
The radius is half of the diameter. Therefore, if the diameter is denoted as $d$, the radius $r$ can be expressed as: $$ r = \frac{d}{2} $$
- Invoke the area formula for a circle
The area $A$ of a circle is given by the formula: $$ A = πr^2 $$
- Substitute the radius in terms of diameter into the area formula
Replace $r$ with $\frac{d}{2}$ in the area formula: $$ A = π \left( \frac{d}{2} \right)^2 $$
- Simplify the area formula
Now simplify the expression: $$ A = π \cdot \frac{d^2}{4} $$ This results in: $$ A = \frac{π}{4} d^2 $$
The area of a circle in terms of its diameter is given by the formula: $$ A = \frac{π}{4} d^2 $$
More Information
This formula allows you to calculate the area of a circle directly from its diameter without needing to find the radius first. π (pi) is a constant approximately equal to 3.14159, which is essential in calculations related to circles.
Tips
- A common mistake is to forget to square the radius when substituting it into the area formula. Always remember that the area involves squaring the radius, which is half the diameter.
