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The radius of a circle is 10 meters. What is the area of a sector bounded by a 45° arc?

45°
r=10 m
Give the exact answer in simplest form.

The radius of a circle is 10 meters. What is the area of a sector bounded by a 45° arc-example-1

2 Answers

9 votes

Final answer:

The area of the sector bounded by a 45° arc in a circle with a 10-meter radius is exactly (25π)/4 m² in simplest form.

Step-by-step explanation:

The question is asking for the area of a sector formed by a 45° arc in a circle where the radius (r) is 10 meters. The formula to find the area of a sector is A = (θ/360)×πr², where θ is the central angle in degrees. In this case, θ = 45°.

First, we convert the angle to radians, since one full circle (360°) is equivalent to 2π radians. Therefore, 45° is (45/360)×2π = π/4 radians.

Now we can calculate the area of the sector as follows:

A = (π/4)×π×10²

A = (π²/4)×100

A = (25π²)/4

Since we want the exact answer in simplest form, we leave π as it is, and the final answer is:

A = (25π)/4 m²

User Sanka Geethanjana
by
8.0k points
6 votes

Answer:

39.269

Step-by-step explanation:

User Hwcverwe
by
7.8k points

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