Question

find the area A of the sector of the circle of radius 10 feet formed by the central angle 1/4 radian

Answer 1

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To find the area of the sector of a circle, we can use the formula:

A = (θ/2π) * πr²

where A is the area, θ is the central angle in radians, and r is the radius of the circle.

In this case, the radius of the circle is given as 10 feet and the central angle is 1/4 radian.

Let's substitute the given values into the formula:

A = (1/4 / 2π) * π(10)²

Simplifying:

A = (1/8π) * 100π

The π cancels out:

A = 100/8

Simplifying further:

A = 12.5

Therefore, the area of the sector of the circle with a radius of 10 feet and a central angle of 1/4 radian is 12.5 square feet.

~ Sun

Answer 2

Step-by-step explanation:

To find the area (A) of a sector, you can use the formula:

\[ A = \frac{\theta}{2\pi} \times \pi r^2 \]

where:

- \( \theta \) is the central angle in radians,

- \( r \) is the radius of the circle.

In this case, \( \theta = \frac{1}{4} \) radians and \( r = 10 \) feet. Plugging in these values:

\[ A = \frac{\frac{1}{4}}{2\pi} \times \pi \times (10)^2 \]

Simplify to find the area.