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A circle has a diameter of
18
m. Find the area of the sector
whose central angle is 135°

Sagot :

Sarah06109

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.

  • r= d/2

The diameter is 18 meters.

  • r= 18 m/2
  • r= 9 m

Now we know all the variables:

  • θ=135
  • r= 9 m

Substitute the values into the formula.

[tex]A=\frac{ 135}{360} * \pi (9)^2[/tex]

Solve the exponent first.

  • (9)²= 9 m *9 m= 81 m²

[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.

  1. Using 3.14 as pi

[tex]A=\frac{243}{8} *3.14 \ m^2[/tex]

[tex]A= 95.3775 \ m^2[/tex]

  1. Using the pi button as pi

[tex]A= 95.42587685 \ m^2[/tex]

The area is 243/8 π, 95.3775, or 95.42587685 square meters.

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