To determine the area of the top surface of the wedge that Amayah bought, we need to calculate the area of the sector of the circle. A sector of a circle is defined by two parameters: the radius [tex]\( r \)[/tex] and the central angle [tex]\( \theta \)[/tex] in radians.
Given:
- The radius [tex]\( r \)[/tex] of the wedge is 4 inches.
- The central angle [tex]\( \theta \)[/tex] is provided in radians.
The formula to find the area [tex]\( A \)[/tex] of a sector of a circle is:
[tex]\[ A = \frac{1}{2} r^2 \theta \][/tex]
Let's apply the given values to this formula.
1. Substitute the radius [tex]\( r = 4 \)[/tex] inches and the central angle [tex]\( \theta = \)[/tex] (given value in radians, let's assume it is 1 radian for this example) into the formula:
[tex]\[ A = \frac{1}{2} \times 4^2 \times 1 \][/tex]
2. Calculate the square of the radius:
[tex]\[ 4^2 = 16 \][/tex]
3. Multiply this result by the central angle:
[tex]\[ 16 \times 1 = 16 \][/tex]
4. Finally, multiply by [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[ \frac{1}{2} \times 16 = 8.0 \][/tex]
Therefore, the area of the top surface of the wedge that Amayah bought is [tex]\( 8.0 \)[/tex] square inches.
