Calculate Circle Area with Radius r=7-5a: Variable Radius Problem

To solve this problem, we'll calculate the area of the circle using the given radius expression. The process involves substituting and simplifying expressions:

• Step 1: Recognize that the area of a circle is given by the formula $A = \pi r^2$, where $r$ is the radius.
• Step 2: Substitute the given expression for the radius: $r = 7 - 5a$.
• Step 3: Calculate $r^2$ by expanding $(7 - 5a)^2$ using the identity for squaring a binomial.

Let's apply these steps:

First, substitute the expression for the radius into the area formula:
$A = \pi (7 - 5a)^2$.

Next, expand $(7 - 5a)^2$ using the distributive property or binomial expansion:
$(7 - 5a)^2 = 7^2 - 2 \cdot 7 \cdot 5a + (5a)^2 = 49 - 70a + 25a^2$.

Substituting back, we find:
$A = \pi (49 - 70a + 25a^2)$.

The area of the circle, simplified, is:
$A = 25\pi a^2 - 70\pi a + 49\pi$.

Therefore, the area of the circle in terms of $a$ is $25\pi a^2 - 70\pi a + 49\pi$.