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Answer:
[tex]\boxed {\boxed {\sf \frac{ 243}{8} \pi , 95.3775, or \ 95.42587686 \ m^2 }}[/tex]
Step-by-step explanation:
When given the central angle in degrees, the formula for sector area is:
[tex]A=\frac{ \theta}{360} * \pi r^2[/tex]
where θ is the central angle and r is the radius.
We are given the diameter, so we must calculate the radius. The radius is half the diameter.
The diameter is 18 meters.
Now we know all the variables:
Substitute the values into the formula.
[tex]A=\frac{ 135}{360} * \pi (9)^2[/tex]
Solve the exponent first.
[tex]A=\frac{ 135}{360} * (81 \ m^2) \pi[/tex]
Solve the fraction.
[tex]A=\frac{ 3}{8} * (81 \ m^2) \pi[/tex]
Multiply the two rational numbers.
[tex]A=\frac{243}{8} \pi \ m^2[/tex]
The answer can be left like this, in terms of pi, or can be multiplied.
[tex]A=\frac{243}{8} *3.14 \ m^2[/tex]
[tex]A= 95.3775 \ m^2[/tex]
[tex]A= 95.42587685 \ m^2[/tex]
The area is 243/8 π, 95.3775, or 95.42587685 square meters.