Infinity

In a square with side 18 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares.

Correct result:

S =  648

Solution:

 S1=182 q=12,q<1 S=S111q S=1821112=648



We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 2 comments:
#
Ann
I don't believe this answer is correct. The ratio (q) to find the area of the next square should be 1/8, not 1/2.

#
Math student
no it is 1/2

avatar









Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

 
We encourage you to watch this tutorial video on this math problem: video1   video2

Next similar math problems:

  • Geometric progression 4
    square_rot_1 8,4√2,4,2√2
  • Calculation
    pocty How much is sum of square root of six and the square root of 225?
  • Terms of GP
    exp_growth What is the 6th term of the GP 9, 81, 729,. .. ?
  • Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1
  • ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  • Square
    ppyth5 Calculate the side of a square with a diagonal measurement 10 cm.
  • Square
    1square Calculate area of the square with diagonal 64 cm.
  • Geometric progression 2
    exp_x There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
  • Right angled
    right-triangle From the right triangle with legs 12 cm and 20 cm we built a square with the same content as the triangle. How long will be side of the square?
  • RT triangle and height
    345 Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
  • Euclid2
    euclid In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
  • Square2
    square_2 Side of the square is a = 6.2 cm, how long is its diagonal?
  • Triangle ABC
    lalala In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
  • Euklid4
    euclid_2 Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
  • Tree trunk
    tram From the tree trunk, the diameter at the narrower end is 28 cm, a beam of square cross-section is to be made. Calculate the longest side of the largest possible square cross-section.
  • Dog
    stvorec_1 Dog is tied to a chain, which is mounted in a corner of the yard. Yard has the shape of a square with a side length of 20 meters. The same long is also dogchain. Are there places in the yard where dog can't reach?
  • Annular area
    medzikrucie2 The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.