Consider circle C with radius 5 cm and a central angle measure of 60°. What fraction of the whole circle is arc RS? What

Question

Consider circle C with radius 5 cm and a central angle measure of 60°. What fraction of the whole circle is arc RS?

What is the approximate circumference of the circle?
cm

What is the approximate length of arc RS?
cm

in progress 0
Jasmine 1 week 2021-09-09T00:42:04+00:00 2 Answers 0

Answers ( )

    0
    2021-09-09T00:43:50+00:00

    Step-by-step explanation:

    What fraction of the whole circle is arc RS?

    • 1/6

    What is the approximate circumference of the circle?

    • 31.4

    What is he approximate length of arc RS?

    • 5.2
    0
    2021-09-09T00:43:53+00:00

    Answer:

    There are a total of 360° in any given circle, so an arc swept out by 60° of that 360° would make up 60/360 = 1/6 of the circle’s circumference.

    The formal for the circumference of a circle comes out of the definition of one of the most famous constants in mathematics: π. π is defined as the ratio between a circle’s circumference and its diameter, or:

    From this definition, we can multiply both sides of the equation by d to obtain

    or, circumference is π times the diameter. To find the diameter, we just need to double the radius, giving us 5 * 2 = 10cm. Usually you’ll see π approximated as 3.14, which is likely what they want you to use here. Using that approximation, we find the circumference to be 3.14 * 10 = 31.4 cm.

    Finally, to get the length of that arc, we just need to take 1/6 of the circumference (since the arc sweeps out 1/6 of the circle), giving us 31.4 * 1/6 ≈ 5.2 cm.

    Step-by-step explanation:

Leave an answer

45:7+7-4:2-5:5*4+35:2 =? ( )