Circle: Extreme Case of Polygons

Q.

The area of a circle is $154cm²$. Find its diameter.

Q.

A circle is a polygon as it is a closed figure.

1. True

2. False

Q.

Draw any circle and mark points $A$, $B$ and $C$ such that $A$ is on the circle, $B$ is in the interior of the circle and $C$ is in the exterior of the circle.

Q. The is a set of points in a plane equidistant from a fixed point.

1. triangle
2. square
3. circle

Q. A circle is a set of points in a plane that are at a fixed from the fixed .

1. distance
2. point
3. displacement
4. line

Q. Diagonals of trapezium $ABCD$ with $AB\parallel DC$ intersect each other at the point $O$. If $AB=2CD$, find the ratio of the areas of triangles $AOB$ and $COD$.

1. $4:1$
2. $3:1$
3. $4:7$
4. $4:3$

Q. Fill in the blanks:
(1) The centre of a circle lies in ___________ of the circle (exterior/interior)
(2) A point whose distance from the centre of a circle is greater than its radius lies in ___________ of the circle
(3) The longest chord of a circle is a ____________ of the circle.
(4) An arc is a ____________ when its ends are the ends of a diameter.
(5) Segment of a circle is the region between an arc and __________ of the circle.
(6) A circle divides the plane, on which it lies in ______________ parts.

Q.

Is a circle an ellipse?

Q. Consider a point A on the circle of radius $\frac{7}{\pi }$ cm as shown in the figure. A ball on point A moves along the circumference until it reaches a point B. The tangent at B is parallel to the tangent at A. What is the distance traveled by the ball? (Consider the ball to be a point object)

Note: The point B in the diagram may not represent its actual position.

1. 7 cm
2. 3.5cm
3. 14cm
4. 28 cm

Q.

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹0.35 per $c{m}^2$ . (Use $\sqrt{3}=1.7$)

1. $₹195$

2. $₹157$

3. $₹162$

4. $₹200$

Q. Two circles intersect as shown in the diagram below. The radii of the circles are 14 cm each and $\angle AOP={45}^{\circ }$​ What is the area of the region shaded in blue?

1. $132.5\pi sq.cm$
2. $156sq.cm$
3. $112sq.cm$
4. $56sq.cm$

Q.

The area of a circle is half the product of its perimeter and its ___.

1. area

2. diameter

3. radius

4. pi

Q.

The perimeter of a triangle is 30 cm and the circumference of its incircle is 88cm. The area of the triangle is ___.

1. $70c{m}^2$

2. $140c{m}^2$

3. $210c{m}^2$

4. $420c{m}^2$

Q.

Statement 1: The area of a quarter circle is one-fourth of that of a circle with same radius.

Statement 2: The circumference of a quarter circle is one-fourth of that of a circle with same radius.

1. Both the statements are false

2. Both the statements are true

3. Statement 1 is true and statement 2 is false

4. Statement 1 is false and statement 2 is true

Q.

On a square handkerchief of side 50 cm, seven non-intersecting circles designs of each radius 7 cm are made. Find the area of the remaining portion of the handkerchief in $c{m}^2$.

1. 1308.6

2. 1423

3. 1452.6

4. 1466

Q. The area of a circular pond is 1 acre find the cost of gravelling a path 4 ft wide around it at $ 1 per square ft
1 acre=4840 sq. yard