Question

A circle of radius 3
units is drawn with
the origin as it's
center. How many
squares of unit
length and integer
coordinate vertices
lie inside or are
intersected by the
circle?​

Answer 1

Step-by-step explanation:

Given:A circle of radius 3 units is drawn with the origin as it's center.

To find:How many squares of unit length and integer coordinate vertices lie inside or are intersected by the circle?

Solution:

To draw the circle of radius 3 units,measure 3 cm with compass put it at the origin(Intersection of both axes) and draw the circle.

The circle intersects x-axis at +3 and -3 by the same way at y-axis.

Now count the number of squares completely lies inside the circle of area 1 unit².

Please see the attached figure.

Total square that completely lies inside the circle :16

Total square that intersected by perimeter of the circle :16

(Not having all vertices integers)

Thus,

Squares of unit length and integer coordinate vertices lie inside the circle are 16 or 0 squares have integer coordinate are intersected by the circle.

Hope it helps you.

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Answer 2

Given :  A circle of radius 3 units is drawn with the origin as it’s center.

To Find : How many squares of unit length and integer coordinate vertices lie inside or are intersected by the circle

Solution:

Vertices lying inside the circle

x² + y² < 3²

=> x² + y² < 9

x = 0 , y = 0 , ± 1 , ± 2

x = ±1  , y = 0,  ± 1 , ± 2

x = ±2  , y = 0,  ± 1 , ± 2

larger square size has side length = 4 .

Hence  4 * 4  = 16  unit squares are inside circle having integral values

So 16 Squares can be formed of unit length and integer coordinate  vertices

Now a boundary of square will be formed outside one larger square of 4*4

so  squares intersecting circles will be (4+1+1)² - 4² = 20

squares of unit length and integer coordinate vertices lie inside are 16 and  are intersected by the circle = 20

Total are  36

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