Circles: Circumference and Area of a Circle

think icon Think & Click: Arc Length and Area of a Sector

Now, you try. Complete the Think & Click activity by looking at each problem below, thinking about it, and then clicking on the question to reveal the solution.

1. Find the arc length and the area of the sector of 75° of a circle with radius 7 ft.

Arc Length equals the quotient “arc measure” over 360 times capital C; Arc Length equals the quotient arc measure over 360 times 2 pi r; Arc Length equals seventy-five-three-sixtieths times 2 pi times 7 equals thirty-five-twelfths times pi approximately equals 9 point 16

The arc length is approximately 9.16 ft.

 

Area of sector equals the quotient arc measure divided by 360 times capital A; Area of sector equals the quotient arc measure divided by 360 times pi r-squared; Area of sector equals seventy-five-three-sixtieths times pi times 7 squared equals two-hundred-forty-five-twenty-fourths times pi approximately equals 32 point 07

The area of the sector is approximately 32.07 ft2.

2. Find the arc length and the area of the sector of 215° of a circle with diameter 50 cm.

r equals one-half d equals one-half times 50 equals 25
The radius is 25 cm.

Arc Length equals the quotient “arc measure” over 360 times capital C; Arc Length equals the quotient arc measure over 360 times 2 pi r; Arc Length equals two-hundred-fifteen-three-sixtieths times 2 pi times 25 equals one-thousand-seventy-five-thirty-sixths pi approximately equals 93 point 81

The arc length is approximately 93.81 cm.

 

Area of sector equals the quotient arc measure divided by 360 times capital A; Area of sector equals the quotient arc measure divided by 360 times pi r-squared; Area of sector equals two-hundred fifteen-three-sixtieths times pi times 25 squared equals twenty-six-thousand-eight-hundred-seventy-five-seventy-seconds times pi approximately equals 1172 point 64

The area of the sector is approximately 1172.64 cm2.

3. Find the arc measure if the arc length is 4.328 ft and the radius is 4 ft.

Arc Length equals the quotient “arc measure” over 360 times capital C; Arc Length equals the quotient arc measure over 360 times 2 pi r; 4 point 3 2 8 equals the quotient x over 360 times 2 pi times 4; 4 point 3 2 8 equals the quotient 8 pi over 360 times x; the quotient 360 over 8 pi, the quotient times 4 point 3 2 8 equals the quotient 360 over 8 pi times the quotient 8 pi over 360, all times x; 62 equals x

The arc measure is 62°.

4. Find the arc measure if the area of the sector is 116.15 in2. and the radius is 11 in.

Area of sector equals the quotient arc measure divided by 360 times capital A; Area of sector equals the quotient arc measure divided by 360 times pi r-squared; 116 point 15 equals the quotient x divided by 360, the quotient times pi times 11 squared; 116 point 15 equals the quotient 121 pi over 360, the quotient times x; the quotient 360 over 121 pi, the quotient times 116 point 15 equals the quotient 360 over 121 pi, the quotient times the quotient 121 pi over 360 times x; 110 equals x

The arc measure is 110°.

5.  Pizzas are defined by the length of their diameters.  If you buy a 16 inch pizza and share it with 5 of your friends (you and 5 friends makes 6 people), how much pizza do you each get in square inches?

r equals one-half d equals one-half times 16 equals 8

A = πr2 = π(8)2 = 64π

Area each person gets = one-sixth times 64 pi equals thirty-two-thirds times pi approximately equals 33 point 51
Each person gets approximately 33.51 in2.


Review Icon Review Worksheet

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