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=S1⋅11−q S=182⋅11−12=648

Try another example


We would be very happy if you find an error in the example, spelling mistakes, or inaccuracies, and please send it to us. We 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.

You need to know the following knowledge to solve this word math problem:


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

Next similar math problems:

  • Annular area
    medzikrucie2 The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
  • Square
    ppyth5 Calculate the side of a square with a diagonal measurement 10 cm.
  • 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?
  • 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?
  • Without Euclid laws
    euclid_1 Right triangle ABC with right angle at the C has a=5 and hypotenuse c=19. Calculate the height h of this triangle without the use of Euclidean laws.
  • Square
    1square Calculate area of the square with diagonal 64 cm.
  • Square2
    square_2 Side of the square is a = 6.2 cm, how long is its diagonal?
  • 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.
  • Calculation
    pocty How much is sum of square root of six and the square root of 225?
  • Geometric progression 4
    square_rot_1 8,4√2,4,2√2
  • Geometric progression
    fractal Fill 4 numbers between 4 and -12500 to form geometric progression.
  • 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.
  • 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.
  • Geometric progression 2
    exp_x There is geometric sequence with a1=5.7 and quotient q=-2.5. Calculate a17.
  • 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.
  • ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  • Six terms
    sequence_geo_3 Find the first six terms of the sequence a1 = -3, an = 2 * an-1