geometry

For this question, please reference the image at:
imgur<dot>com/KSYAN6T

All circles in the dartboard have the same center.
Each circle has half the radius of the previous circle.
The colors alternate orange-white-orange-white-etc. forever.

How much of the dartboard is colored orange?

  1. 👍 0
  2. 👎 0
  3. 👁 152
  1. the radii form a geometric sequence
    r, r/2, r/4, ...
    The orange rings have areas that form another sequence:
    πr^2 - π(r/2)^2, π(r/4)^2 - π(r/8)^2, ...
    = πr^2 (3/4 + 3/64 + ...)
    the sum of all those areas is thus
    πr^2 (3/4)/(1 - 1/16) = 4/5 πr^2
    so, 4/5 of the dartboard is orange

    1. 👍 0
    2. 👎 0
    👨‍🏫
    oobleck

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math(problem solving)

    Four darts are thrown at this dartboard. If all four darts hit the board, how many different point totals are possible? there are 4 circles with point totals: working out from the middle bulls eye.. bulls eye = 9 2nd circle = 7

  2. math

    Two circles of radius 4 are tangent to the graph of y^2=4x at the point (1,2). Find the equation of these two circles.

  3. Physics

    A dart is thrown at a dartboard 2.37 m away. When the dart is released at the same height as the center of the dartboard, it hits the center 0.447 sec. At what angel relative to the floor was the dart thrown.

  4. Science

    A scientist from the United States conducts an experiment using miles per hour to measure speed. Why might this be confusing for scientists in other countries? A) Scientists in other countries don't usually perform experiments

  1. Math

    A 10-in2 section of a 25-in2 dartboard is painted red. If a dart lands at random on the dartboard, what is the probability that it lands in the section painted red?

  2. Algebra

    Click on "Explain" if you need help. A dart hits the circular dartboard shown below at a random point. Find the probability that the dart lands in the shaded square region. The radius of the dartboard is 5in, and each side of the

  3. Trig

    Three circles with radii of 4, 5, and 6 cm, respectively, are tangent to each other externally. Find the angles of the triangle whose vertexes are the centers of the circles.

  4. geometry

    Question 4.4. Which is true about a rotation? (Points : 1) The image and preimage are congruent. The image overlaps the preimage. The image is larger than the preimage. The image is smaller than the preimage. Question 5.5.

  1. trig

    Two circles of radii 5 and 3 cm, respectively, intersect at two points. At either point of intersection, the tangent lines to the circles form a 60◦ angle, as in Figure 2.2.4 above. Find the distance between the centers of the

  2. Algebra 2

    Make a table with a process column to represent each pattern. Write an expression for the number of circles in the Nth figure. The first figure is 5 circles long and 2 circles wide, the second 5 circles long and 3 circles wide.

  3. Physics

    (a) A 2.20 cm high insect is 1.24 m from a 135 mm focal-length lens. What is the image distance? mm How high is the image? cm What type is it? (Select all that apply.) The image is upright. The image is inverted. The image is

  4. Math

    Circle S and Circle U are congruent circles. The figure shows two circles with their center labeled as Upper S and Upper U. The two circles overlap each other such that they intersect at points Upper R and Upper T. D Name three

You can view more similar questions or ask a new question.