The illustration is omitted. Please see the attachment below.
Answer:
The area of the shaded sector is 144π square units.
Step-by-step breakdown:
Given:
The central angle for the sector is, 
The circle's radius is, 
The area of a sector with radius 'R' and angle
can be determined with:

Substituting
gives

Thus, the area of the shaded sector calculates to 144π square units.
Indeed, a fare of $40 is a fair charge for the cab ride.
Explanation
Sheri's cab fare totaled $32, with a gratuity rate of 20%.
The gratuity amount is: 
Thus, the total cab fare including gratuity is: 
Since Sheri issued a $40 check to the cab driver, it indicates she provided ($40 - $38.40) or an extra $1.60 to the cab driver. Consequently, the $40 payment is reasonable for the cab fare.
You can utilize the Pythagorean theorem expressed as a^2 + b^2 = c^2... if b is unknown, you can rearrange the formula. Hence, c^2 - a^2 = b^2. Squaring 47 gives 2209 and squaring 13 yields 169... Subtracting gives you 2209-169, which results in 2040. Taking the square root of that yields approximately 45.166359, which can be rounded to 45 or as 45.167 when expressed to two decimal places. I hope this helps!:)
Answer:
Kayla is right; the center constitutes a fixed point located at the sphere's core.
Step-by-step explanation:
Kayla is indeed correct, whereas Raymond is mistaken since a point itself cannot represent a radius; a radius is defined as the line segment stretching from the center to the surface.
The center is indeed the stable point positioned at the center of the sphere.