# Free Circles 02 Practice Test - 4th Grade

The figure is of a circle with its center at O. The line PQ is the:

A.

Diameter of the circle

B.

Radius of the circle

C.

Chord of the circle

D.

Tangent of the circle

#### SOLUTION

Solution : A

The line PQ is the diameter of the circle. A diameter of a circle is a line segment that passes through centre of the circle and whose endpoints lie on the circle.

Which is the correct relation of radius and diameter?

A.

r = 2D

B.

D = 2r

C.

r = D

D.

r = 3D

#### SOLUTION

Solution : B

Diameter = 2 × radius (or) twice the radius
D = 2r is the correct relation between them.

The region inscribed by a chord and two radii having endpoints at the end of the chord will be a/an ___.

A.

isosceles triangle

B.

scalene triangle

C.

square

D.

parallelogram

#### SOLUTION

Solution : A

The shaded triangle in the figure is an isosceles triangle.
A triangle in which two sides are equal is called an isosceles triangle. Here, the two equal sides are the radii of the circle OA and OB.

Identify longest chords in the given figure.

A.

B.

AB, BC

C.

AB, CD

D.

#### SOLUTION

Solution : D

The chords of the given circle are AB, CD, BC and AD.

The diameter of a circle is its longest chord.

Since BC and AD pass through the center(O) of the circle, they are the diameters of the circle and hence, the longest chords.

Which of the following cannot be the length of chord of a circle of radius 4 cm?

A.

12 cm

B.

6.5 cm

C.

6 cm

D.

7 cm

#### SOLUTION

Solution : A

Given that

The radius of a circle is 4 cm.

The diameter of the circle = 4 × 2 = 8 cm

The diameter is the longest chord of a circle. Hence, the length of any chord cannot be more than 8 cm.

A circle with center O is shown below. The line segment OA is the ____ of the circle.

A.

diameter

B.

C.

chord

D.

segment

#### SOLUTION

Solution : B

The radius of a circle is a line segment joining the center of the circle to any point on the circumference of the circle.

The line segment OA is the radius of the circle.

Find the diameter of a circle of radius 48 cm.

A.

98 cm

B.

96 cm

C.

100 cm

D.

95 cm

#### SOLUTION

Solution : B

Given that

The radius of a circle = 48 cm

The diameter of a circle = radius × 2

On substituting the values we get;

The diameter of the circle = 48 × 2 = 96 cm

What will be the radius of a circle  whose diameter is 36 cm?

A.

11 cm

B.

66 cm

C.

16 cm

D.

18 cm

#### SOLUTION

Solution : D

Given that

The length of the diameter of a circle = 36 cm

We know that, radius of a circle = Diameter2

On substituting the values we get:

Radius of circle = 362=18 cm

What will be the diameter of a circle of radius 18 cm?

A.

36 cm

B.

18 cm

C.

9 cm

D.

39 cm

#### SOLUTION

Solution : A

Given that

The radius of the circle = 18 cm

The diameter of the circle = radius × 2

On substituting the values we get:

The diameter of the circle = 18 × 2 = 36 cm

If the radius of a circle is a multiple of 3, then the diameter will be a multiple of

A.

3

B.

6

C.

both 3 and 6

D.

5

#### SOLUTION

Solution : C

Given that

The radius of a circle is a multiple of 3.

So, the radius of the circle can be 3n, where n is any natural number.

Now, Diameter of a circle = radius × 2 = 3n × 2 = 6 ×n

Hence, the diameter of the circle is a multiple of both 3 and 6.