Find the area of the sector with angle 69 degrees and radius 3 cm, using pi = 22/7. Express your answer as a…

Question

Find the area of the sector with angle 69 degrees and radius 3 cm, using pi = 22/7. Express your answer as a mixed number.

ScanSolve AI Tutor · Accepted Answer

Here's how to find the area of the sector for Q7.

Identify the given values for the sector.
The angle of the sector is $\theta = 69^\circ$ .
The radius of the sector is $r = 3 \text{ cm}$ .
We are instructed to use $\pi = \frac{22}{7}$ .
Apply the formula for the area of a sector.
The formula for the area of a sector is $A = \frac{\theta}{360^\circ} \pi r^2$ .
$A = \frac{69}{360} \times \frac{22}{7} \times (3 \text{ cm})^2$ $A = \frac{69}{360} \times \frac{22}{7} \times 9 \text{ cm}^2$
Simplify the expression.
First, simplify the fraction $\frac{69}{360}$ by dividing both numerator and denominator by their greatest common divisor, which is 3.
$\frac{69 \div 3}{360 \div 3} = \frac{23}{120}$
Now substitute this back into the area calculation:
$A = \frac{23}{120} \times \frac{22}{7} \times 9 \text{ cm}^2$
Multiply the numerators and denominators:
$A = \frac{23 \times 22 \times 9}{120 \times 7} \text{ cm}^2$ $A = \frac{4554}{840} \text{ cm}^2$
Simplify the fraction by dividing both numerator and denominator by their greatest common divisor. Both are divisible by 6.
$\frac{4554 \div 6}{840 \div 6} = \frac{759}{140} \text{ cm}^2$
Convert the improper fraction to a mixed number.
Divide 759 by 140:
$759 \div 140 = 5 \text{ with a remainder of } 59$
So, the mixed number is $5 \frac{59}{140}$ .

The area of the sector is $5 \frac{59}{140} \text{ cm}^2$ .

Find the area of the sector with angle 69 degrees and radius 3 cm, using pi = 22/7. Express your answer as a mixed number.