The exact area of the sector of a circle with a 16 cm radius and having an angle of 45° at the center in terms of π is 32π cm².
What is the meaning of the sector of a circle?
The sector is defined as a portion of a circle made up of the circle's arc and two radii. It's a section of the circle made up of a piece of the circumference (arc) and the circle's radii at both ends. A slice of pizza or a pie can be compared to the form of a circle sector.
How do we determine the area of a sector of a circle?
The area of a sector of a circle with radius r units, and the angle subtended by the sector at the center θ (in degrees), is given by the formula,
Area = πr²(θ/360°)
How do we solve the given question?
We are asked to find the area of a sector of a circle with a radius of 16 centimeters, and the angle subtended at the center = 45°.
We use the formula discussed above: Area = πr²(θ/360°),
with r = 16 cm, θ = 45°.
Substituting these values in the formula, we get:
Area = π(16²)(45°/360°) cm² = π*256*(1/8) cm² = π*32 cm² = 32π cm².
∴ The exact area of the sector of a circle with a 16 cm radius and having an angle of 45° at the center in terms of π is 32π cm².
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