How big of a circle can fit in a rectangle?

1 Expert Answer The diameter can only be as long as the shorter sides of the rectangle. Let’s say we have s 5″ x 7″ in rectangle; the diameter can be up to 5″. Anything longer than that wouldn’t fit.

What is the ratio of the area of a circle to the area of a square?

5π:18
So the area of the circle is πr2=10×2π. So the ratio of the area of the circle to the area of the square is 10×2π:36×2, which is equivalent to 5π:18, as required.

How many circles are in a rectangle?

If we make 257 the vertical dimension, then the rectangle is a bit over 144⋅r units tall, and a bit over (2+49√3)⋅r units wide. So we can arrange the circles in 50 columns that alternate between 72 and 71 circles, for 25⋅72+25⋅71=3575 circles.

Will a rectangle fit in a circle?

Actually – every rectangle can be inscribed in a (unique circle) so the key point is that the radius of the circle is R (I think). One of the properties of a rectangle is that the diagonals bisect in the ‘center’ of the rectangle, which will also be the center of the circumscribing circle.

What is the ratio of a circle?

Circles are all similar, and “the circumference divided by the diameter” produces the same value regardless of their radius. This value is the ratio of the circumference of a circle to its diameter and is called π (Pi).

What is the ratio area of a circle?

In geometry, the area enclosed by a circle of radius r is πr2. Here the Greek letter π represents the constant ratio of the circumference of any circle to its diameter, approximately equal to 3.1416.

How many circles can fit inside a rectangle?

The calculator below estimates the maximum number of circles that may fit within a rectangle. The calculator can be used to calculate Input the rectangle inside dimensions – height and width and the circles outside diameters. Default values are for 0.5 inch circles inside a 10 inch x 10 inch square.

What is the radius of the circle inscribed in the rectangle?

From the figure, we can see, the biggest circle that could be inscribed in the rectangle will have radius always equal to the half of the shorter side of the rectangle. So from the figure, Attention reader! Don’t stop learning now.

How do you convert a circle to a square?

Convert the area of a circle into an rectangle shaped area of the same size. Works much the same way as a circle to square conversion but you will have to enter the width of the rectangle in addition to the circle’s diameter. Circle Formula’s Radius R = D ÷ 2 where R = radius, D = diameter Area; A = π * D² ÷ 4

How do you find the point where a rectangle touches a circle?

The point where rectangle touches the circle is | R − a | and | R − b | away from x and y axes, where a and b are lengths of sides of the rectangle and R is the radius of the circle. This leads to the equation (R − a)2 + (R − b)2 = R2, which has solutions R1, 2 = a + b ± √2ab.