# Free Areas Related to Circles 01 Practice Test - 10th Grade

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 cm2.

__

#### SOLUTION

Solution :

Area of a square = side2
Side of the square = 50 cm
Area of square Handkerchief = 502 = 2500 cm2
Area of circles = π×r2
Radius of the circle = 7 cm

Total area of circles = 7 x 22772 = 1078cm2

Remaining area = 2500 - 1078 = 1422 cm2

The given figure is a sector of a circle of radius 20 cm. Find the perimeter of the sector.
(Take π = 3.14)

A.

55.25 cm

B.

60.93 cm

C.

65.48 cm

D.

70.17

#### SOLUTION

Solution : B

The circumference i.e , perimeter of a sector of angle P of a circle with radius R is given by

P360 ×2πr +2R

=P360 × 2π R+2R

=60360 × 2π (20)+2(20)

= 20.93 + 40

= 60.93 cm

The area of a sector (in cm2 )of a circle with radius 6 cm if angle of the sector is 70 will be __ cm2. ( Take π = 227)

#### SOLUTION

Solution :

Given that radius r = 6 cm
θ = 70
Area of sector of an angle θ with radius r
=θ360 ×  π × (r)2
= 70360 ×  227  ×  62
= 22 cm2

ABCD is a flower bed. If OA = 21m and OC = 14m. Find the area of the bed in m2.

A.

180.30

B.

921

C.

190

D.

192.50

#### SOLUTION

Solution : D

Area of a sector with angle θ is given by =θ360° × π × r2 ( where θ is the angle made by the sector )
Required area = Area of sector OABO – Area of sector OCDO

The angle formed by the sector OABO and sector OCDO = 90°
=90360×227×(21)290360×227×(14)2
=14×227×{(21)2(14)2}
=14×227×{(35)(7)}  [a2b2=(a+b)(ab)]
=192.50 m2

State true or false.
If the radius of a circle is 7π cm, then the area of the circle in cm2 is 49π2.

A.

True

B.

False

#### SOLUTION

Solution : B

A = πr2
Given  r = 7π cm

A=π×7π×7π

=49 cm2

A circle is inserted inside a square, such that the edge of the circle touches the sides of the square.If X = 14 cm, the area of the shaded portion will be __sq.cm.

#### SOLUTION

Solution :

Here we are asked to find the area of the shaded area. The area of the shaded area should be the difference between the area of the square and the area of the circle.

Here we are given the side of the square, x = 14 cm
The   area of the square is = side2 = x2 = 142

= 196cm2

Therefore the radius of the circle will be, r =d2

r = 142 = 7 cm

Area of the circle,

A=π×r2                      (use π = 22/7)

= (227)×72   = 154 cm2

Area of the shaded portion = Area of the square - Area of the circle

= 196 - 154 =42 cm2

Therefore the area of the shaded portion will be 42 cm2

State true or false.
Area of a circle is inversely proportional to the radius of circle.

A.

True

B.

False

#### SOLUTION

Solution : B

Area of a circle is directly proportional to the square of the radius of circle.

An umbrella has 8 ribs which are equally spaced. Assuming the umbrella to be a flat circle of radius 42 cm, find the area in cm2 between the two consecutive ribs of the umbrella.

___

#### SOLUTION

Solution :

8 ribs implies angle subtend between consecutive ribs = 3608 = 45 .

Area between consecutive ribs = θ360×π×(radius)2
45360 × 227 ×  422 = 693 cm2

Tick the correct answer in the following:
Area of a sector of angle p (in degrees) of a circle with radius R is

A. p180×2πR
B. p180×πR2
C. p360×2πR
D. p720×2πR2

#### SOLUTION

Solution : D

Area of a sector of angle p=p360×πR2=p360×22×πR2=p720×2πR2

OACB is a quadrant of a circle with centre O and radius 7 cm. It OD = 4cm, then find area of shaded region.

___

#### SOLUTION

Solution :

For the quadrant θ = 90°
Area of the quadrant  = θ360°×π(r)2
Area of quadrant OACB =  90360 ×  227  (7)2 =  772