To solve the given problem, let's first recall the necessary formulas for the area and circumference of a circle.
Given a circle with:
- Diameter [tex]\( d = 6 \)[/tex] units
1. Calculate the Radius:
The radius [tex]\( r \)[/tex] is half of the diameter:
[tex]\[ r = \frac{d}{2} = \frac{6}{2} = 3 \text{ units} \][/tex]
2. Calculate the Area:
The formula for the area [tex]\( A \)[/tex] of a circle is:
[tex]\[ A = \pi r^2 \][/tex]
Substituting the radius into the formula:
[tex]\[ A = \pi (3)^2 = 9\pi \text{ square units} \][/tex]
3. Calculate the Circumference:
The formula for the circumference [tex]\( C \)[/tex] of a circle is:
[tex]\[ C = \pi d \][/tex]
Substituting the diameter into the formula:
[tex]\[ C = \pi (6) = 6\pi \text{ units} \][/tex]
4. Sum the Area and the Circumference:
We need to find the value of [tex]\( b + c \)[/tex], where:
[tex]\[ b = \text{area} = 9\pi \][/tex]
[tex]\[ c = \text{circumference} = 6\pi \][/tex]
Adding [tex]\( b \)[/tex] and [tex]\( c \)[/tex]:
[tex]\[ b + c = 9\pi + 6\pi = 15\pi \][/tex]
Therefore, the value of [tex]\( b + c \)[/tex] is:
[tex]\[ \boxed{15\pi} \][/tex]
