The area of the circle that can be inscribed in a square of 6cm is

Transcript Question 9 The area of the circle that can be inscribed in a square of side 6 cm is (A) 36 π cm2 (B) 18 π cm2 (C) 12 π cm2 (D) 9 π cm2 Since circle is inscribed in the square Diameter of circle = Side of square = 6 cm Thus, Radius = 3 cm Now, Area of circle = 𝜋r2 = 𝜋(3)2 = 9𝜋 cm2 So, the correct answer is (D) Show More

We've seen that when or the length of the square's side. Now we'll see that the same is true when the circle is inscribed in the square. Problem 1 A circle with radius ‘r’ is inscribed in a square. Find formulas for the square’s side length, diagonal length, perimeter and area, in terms of r. Strategy In solving the similar problem of Here, a similar key insight is that the circle's radius is equal to half the square's side length. Since the circle is inscribed in the square, the square's side is The radius forms a 90° angle with one side of the square. Thus, it is parallel to the adjacent side of the square. This is true for the other radii, as well. That means that the quadrilateral formed by two radii and two adjacent sides of the square is also a square. In this new small square, the side is equal to the radius. We can do this for each of the other 4 sides of the larger, outer square. In each one of them, the radii will form smaller squares. In the smaller squares, the sides are all equal to the radius. The sides of two such adjacent small squares form the side of the larger outer square. Since each one of the smaller square's sides is equal to r, the side of the outer square is 2r. Formal proof: (1) OA ⊥ AB //Given, AB is tangent to circle O, a tangent line is perpendicular to the radius (2) m∠OAB=90° //Definition of perpendicular line (3) m∠ABC=90° //All interior angles of a square are right angles (4) OA||CB //Converse Consecutive Interior Angles Theorem (5) OC ⊥ CB...

Example 1: Find the perimeter of the square. When a circle is inscribed in a square, the diameter of the circle is equal to the side length of the square. So, the side length of the square is 6 cm. The perimeter P of a square with side length s is given by P = 4 s . Substitute 6 for s in P = 4 s . P = 4 ( 6 ) = 24 The perimeter of the square is 24 cm. Example 2: What is the area of a circle that is inscribed in a square of area 64 square units? When a circle is inscribed in a square, the length of each side of the square is equal to the diameter of the circle. That is, the diameter of the inscribed circle is 8 units and therefore the radius is 4 units. The area of a circle of radius r units is A = π r 2 . Substitute r = 4 in the formula. A = π ( 4 ) 2 = 16 π ≈ 50.24 Therefore, the area of the inscribe circle is about 50.24 square units.

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SOLUTION: What is the area of a circle if it is inscribed in a square? The radius of the circle is 6cm. The Height of the square is 14cm. and the length of the square is 12cm. SOLUTION: What is the area of a circle if it is inscribed in a square? The radius of the circle is 6cm. The Height of the square is 14cm. and the length of the square is 12cm. You can You have a rather serious terminology problem for starters. How can you have a square that has a 'height' different from its 'length'? A square, by definition, has 4 equal sides. So what you really have is a rectangle. Having said all that, the details of the dimensions of the quadrilateral in which the circle is inscribed is irrelevant information. You are given that the radius of the circle is 6cm, and that is all the information required to calculate the area of a circle: , or in your case: . You do the math. Leave the answer in terms of unless you were instructed to provide a numerical approximation to some specified precision.