MO SK/CZ Z9–I–3

John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.

Result

D =  10 cm

Solution:

r2=(8/2)2+(r2)2 r2=16+r24r+4 0=204r r=20/4=5 cm D=2 r=2 5=10=10  cm r^2 = (8/2)^2+(r-2)^2 \ \\ r^2 = 16+r^2-4r+4 \ \\ 0 = 20-4r \ \\ r = 20/4 = 5 \ cm \ \\ D = 2 \cdot \ r = 2 \cdot \ 5 = 10 = 10 \ \text{ cm }



Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!





Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Showing 1 comment:
#
Math student
I need more explanation as to where these equations are coming from.

avatar









Tips to related online calculators
Looking for help with calculating roots of a quadratic equation?
Do you have a linear equation or system of equations and looking for its solution? Or do you have quadratic equation?
See also our trigonometric triangle calculator.
Pythagorean theorem is the base for the right triangle calculator.

Next similar math problems:

  1. Pendulum
    kyvadlo Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm.
  2. A mast
    stoziar_1 A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken?
  3. Thunderstorm
    blesk The height of the pole before the storm is 10 m. After a storm when they come to check it they see that on the ground from the pole blows part of the column. Distance from the pole is 3 meters. At how high was the pole broken? (In fact, a rectangular tria
  4. Chord
    tetiva2_1 It is given to a circle k(r=6 cm) and the points A, B such that / AB / = 8 cm lies on k. Calculate the distance of the center of circle S to the midpoint C of the segment AB.
  5. Center traverse
    trianles It is true that the middle traverse bisects the triangle?
  6. Fifth of the number
    numbs_5 The fifth of the number is by 24 less than that number. What is the number?
  7. Holidays - on pool
    pool_4 Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
  8. Circle's chords
    twochords In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.
  9. Find radius
    numbers_49 Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
  10. Disc
    vysek.JPG Circumference of the disk is 78.5 cm. What is the circumference of the circular arc of 32° on the disc?
  11. Median in right triangle
    rt_triangle In the rectangular triangle ABC has known the length of the legs a = 15cm and b = 36cm. Calculate the length of the median to side c (to hypotenuse).
  12. Inscribed circle
    vpisana The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
  13. A truck
    truck_11 A truck departs from a distribution center. From there, it goes 20km west, 30km north and 10km west and reaches a shop. How can the truck reach back to the distribution center from the shop (what is the shortest path)?
  14. Sales off
    sale_6 The price has decreased by 20%. How many percents do I have to raise the new price to be the same as before the cut?
  15. Chord 5
    kruhy It is given circle k / S; 5 cm /. Its chord MN is 3 cm away from the center of the circle . Calculate its length.
  16. Calculate
    equilateral_triangle2 Calculate the length of a side of the equilateral triangle with an area of 50cm2.
  17. Cows
    cow_3 Agricultural cooperative has increased the number of housed cows by 14% to 285 units. By how many cows increased agricultural cooperative the number of cows?