Circle Inscribed in a Square

Q. A Circle is inscribed in a square. It means that the circle is

1. Touching the square
2. Outside the square
3. Inside the square

Q.

The centre of a circle lies in ____________ of the circle. (exterior/ interior)

Q.

The diameter of a circular park is $74m.$ A uniform path $3m$ wide runs around outside$.$ Find the cost of levelling the path at $₹15.50$ per square meter$.$

Q. A Circle is inscribed in a Square. The side length of the square is 10 cm. The ratio of the circumference of circle to the Perimeter of square is

1. $\frac{\pi }{2}$
2. $\frac{\pi }{3}$
3. $\frac{\pi }{4}$

Q. A circle is inscribed in a square whose sides have a length of 14 cm each as shown in the figure given below. Find the area of the portion that is shaded in green.

1. 196 sq cm
2. 420 sq cm
3. 220 sq cm
4. 42 sq cm

Q. Given a Circle is inscribed in a square of side each 10 cm. What is the ratio of the area of the circle to the area of the square?

1. $\frac{\pi }{2}$
2. $\frac{\pi }{6}$
3. $\frac{\pi }{4}$
4. $\frac{\pi }{8}$

Q. A circle of radius $\sqrt{7}$ cm is inscribed in a square. Find the area of the shaded region. $(\text{use}\pi =\frac{22}{7})$

${\text{cm}}^2$

Q. What is the area of a circle that is inscribed in a square of side 4 m?

1. $2\pi {\text{m}}^2$
2. $\pi {\text{m}}^2$
3. $4\pi {\text{m}}^2$
4. $8\pi {\text{m}}^2$

Q. A Circle is inscribed in a square. What would be the ratio of area of the circle to the area of square if the sides of square were changed to $S$ ?

1. $\frac{\pi }{6}$
2. $\frac{\pi }{4}$
3. $\frac{\pi }{2}$

Q. A Circle is inscribed in a square of side 10 units. What would be the ratio of the circumference of the circle to the perimeter of the square if the sides of the square were changed to S?

1. $\frac{\pi }{6}$
2. $\frac{\pi }{4}$
3. $\frac{\pi }{3}$
4. $\frac{\pi }{2}$

Q. If a circle is inscribed in a square, then

1. $\frac{\text{Area of the circle}}{\text{Area of the square}}=\frac{\pi }{2}$
2. $\frac{\text{Area of the circle}}{\text{Area of the square}}=\frac{\pi }{4}$
3. $\frac{\text{Circumference of the circle}}{\text{Perimeter of the square}}=\frac{\pi }{4}$
4. $\frac{\text{Circumference of the circle}}{\text{Perimeter of the square}}=\frac{\pi }{2}$

Q. Sides of a square in inscribed circle are

1. Perpendicular to circle
2. Parallel to circle
3. Tangent to the circle
4. Both (a) and (b) above

Q.

Find perimeter of the square, if radius of the circle is 3 cm.
cm

Q.

The given figure shows a semi - circle :

The semicircle has a circumference of 12 cm and the radius is 4 cm. Find the ratio between the circumference and the diameter if this is converted into a full circle.