Circles Lesson

What is a circle?

• A circle can be defined as a 2D figure formed by a set of points that are adjacent to each other and are equidistant from a fixed point.

• The fixed point in this curved plane figure is called the center of the circle i.e. the fixed point from which all points on the boundary of the circle are equidistant.

​Radius vs Diameter

Radius

The distance from the centre of a circle to the outside.

The radius of the circle (r) is half the diameter (d) of the circle.  

The plural of radius is radii.

​Diameter

The distance across the circle going through the centre.

The diameter is twice the radius i.e. d=2r

• Diameter = Circumference/π (used when the circumference is given)

• Diameter = Radius × 2 (used when the radius is given)

• Diameter = 2√(Area/π) (used when the area of the circle is given)

Multiple Choice

The distance across a circle through the center is called the_______________.

• radius

• circumference

• diameter

• area

Multiple Choice

Given a circle with a diameter of 10 m, what is the radius?

• 10 m

• 5 m

• 20 m

• 15 m

Multiple Choice

What is twice as long as a radius

• Center

• Diameter

• Tanget

• Arc

Multiple Choice

Which segment is a radius?

• LM

• DC

• BD

• ML

Circumference

• Circumference is the distance around a circle i.e. it's perimeter

• π which is 22/7 or 3.14 is the ratio of a circle's circumference to its diameter,

• ​Circumference of a circle formula = 2πr

• When the diameter is given: Circumference of a circle formula = π × D

Multiple Choice

What is the name for the distance around a circle?

• Diameter

• Radius

• Circumference

• Chord

Multiple Choice

PI equals

• 22/7

• 3.14...

• both

• neither

Multiple Select

Which of the following are formulas for circumference? (check all that apply)

• $$\pi d$$

• $$2\pi r$$

• $$\pi r^2$$

• $$2\pi r^2$$

Multiple Choice

What is the diameter of a circle with a circumference of 21.98 cm? (use 3.14 for pi) 

• 8 cm

• 7 cm

• 4 cm

• 11 cm

Circle, Semi-circle and Quadrant: Area & Perimeter

• Semi circle - Half of a circle. Could be considered a sector where the circle has been split by the diameter.

• Quadrant - A quarter of a circle, created by two perpendicular radii.

• Area is the space covered by the inside of the figure

Multiple Choice

The space contained inside of a circle is called the...

• radius

• diameter

• circumference

• area

Multiple Choice

What is the equation for finding the area of a circle?

• $$A=\pi r^2\$$

• $$A=\pi dh$$

• $$A=\pi d$$

• $$A=2\pi r$$

Multiple Choice

A wire is looped in the form of a circle of radius 35 cm. If it is re-bent in the form of a square, what will be the length of each side of the square?

• 52 cm

• 55 cm

• 34 cm

• 65 cm

Multiple Choice

The cost of fencing a semi-circular garden of radius 14 m at $10 per metre is 

• Rs. 985

• Rs. 790

• Rs. 720

• Rs. 2085

Multiple Choice

In figure, the radius of quarter circular plot taken is 2 m and radius of the circular flower bed is 2 m. Find the area of the remaining field.

• 52.26 sq m

• 22.6 sq m

• 22.86 sq m

• 99.86 sq m

Multiple Choice

The radius of a circle is 14 cm. Find the radius of the circle whose area is double of the area of the circle.

• $$14\ \ \sqrt[]{2}\ \ cm$$  

• 14 cm

• 52 cm

• $$17\ \sqrt[]{7}\ cm$$  

Multiple Choice

Find the area of the shaded part given that the diameter of the inner circle is 21 cm and the uniform width of the shaded part is 10.5 cm.

• 2525.5 sq cm

• 1039.5 sq cm

• 2079 sq cm

• 1035 sq cm

Multiple Choice

A horse is tied to a pole in a park with a string 21 m long. Find the area over which the horse can graze.

• 3692 sq m

• 1386 sq m

• 485 sq m

• 5862 sq m