Check Your Skills Answer Key

  1. 49π

    The formula for area is A = πr2. The radius is 7, so the area is π(7)2 = 49π.

  2. 17

    Circumference of a circle is either C = 2πr or C = πd. The question asks for the diameter, so use the latter formula: 17π = πd. Divide by π, and you get 17 = d.

  3. 10π

    The link between area and circumference of a circle is that they are both defined in terms of the radius. Area of a circle is A = πr2, so you can use the area of the circle to find the radius: 25π = πr2, so r = 5. If the radius equals 5, then the circumference is C = 2π(5), which equals 10π.

  1. 3π

    If the central angle of the sector is 270°, then it is 3/4 of the full circle, because . If the radius is 2, then the area of the full circle is π(2)2, which equals 4π. If the area of the full circle is 4π, then the area of the sector will be 3/4 × 4π, which equals 3π.

  2. 240°

    To find the central angle, you first need to figure out what fraction of the circle the sector is. You can do that by finding the circumference of the full circle. The radius is 3, so the circumference of the circle is 2π(3) = 6π. That means the sector is 2/3 of the circle, because . That means the central angle of the sector is 2/3 × 360°, which equals 240°.

  3. 8π

    Begin by finding the area of the whole circle. The radius of the circle is 10, so the area is π(10)2, which equals 100π. That means the sector is 2/5 of the circle, because . You can find the circumference of the whole circle using C = 2πr = 2π(10) = 20π. You can find the arc length of the sector by taking 2/5 × 20π = 8π. The arc length of the sector is 8π.