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Area and Circumference of a Circle Worksheet

Area and Circumference of a Circle Worksheet
  • Page 1
 1.  
The diameter of a circular garden is 32 m. What is the new circumference of the garden, if its radius is decreased by 6 m? [ Use π = 3.14]
a.
66.80 m
b.
125.60 m
c.
64.80 m
d.
62.80 m


Solution:

The diameter of the circular garden = 32 m.

So, the radius of the circular garden = diameter / 2 = 32 / 2 = 16 m.

If the radius is decreased by 6 m, then the new radius = 16 - 6 = 10 m.

The new circumference of the garden = 2 × π × new radius.
[Formula.]

= 2 × 3.14 × 10
[Substitute the values.]

= 62.80 m.
[Multiply.]

So, the new circumference of the garden = 62.80 m.


Correct answer : (4)
 2.  
A circular park of radius 300 yd has a circular pavement around it. What is the area of the pavement, if the width of the pavement is 4 yd? [Use π = 3.14]
a.
2426π yd2
b.
7248 yd2
c.
2416π yd2
d.
None of the above


Solution:

Area of a circle with radius r = πr2
[Formula.]

Area of the circular park with radius 300 yd = π(3002).

Area of the park along with the pavement = π(r + 4)2 = π(300 + 4)2 = π(3042).

Area of the pavement = area of the park along with the pavement - area of the park.

Area of the pavement = π(304)2 - π(300)2 = π(3042 - 3002).

= π(304 - 300)(304 + 300)
[(a2 - b2) = (a +b)(a - b).]

= π(4)(604)
[Simplify.]

= 2416π

So, the area of the pavement is 2416π yd2.


Correct answer : (3)
 3.  
What is the area of the shaded region in the figure?[Use π = 3.14]

a.
177.7 cm2
b.
172.7 cm2
c.
127.7 cm2
d.
None of the above


Solution:

Radius of the bigger circle = 8 cm and the radius of the smaller circle = 3 cm.

Area of the bigger circle = π x (radius of the bigger circle)2
[Formula.]

= 3.14 x 82
[Substitute the value of the radius.]

= 3.14 x 8 x 8
[Expand 82 as 8 x 8.]

= 200.96 cm2
[Multiply.]

Area of the bigger circle = 200.96 cm2.

Area of the smaller circle = π x (radius of the smaller circle)2
[Formula.]

= 3.14 x 32
[Substitute the radius of the smaller circle.]

= 3.14 x 3 x 3
[Expand 32 as 3 x 3.]

= 28.26 cm2
[Multiply.]

Area of the smaller circle = 28.26 cm2

Area of the shaded region = area of the bigger circle – area of the smaller circle.

= 200.96 - 28.26
[Substitute the values.]

= 172.7
[Subtract.]

So, area of the shaded region is 172.7 cm2.


Correct answer : (2)
 4.  
The radius of a sector of a circle is 2 cm and its central angle is 90 degrees. Calculate the perimeter of the sector.
a.
4 cm
b.
π cm
c.
(4 + π) cm
d.
(2 + π) cm


Solution:

Perimeter of a sector of a circle = 2 × radius + arc length.
[Formula.]

= 2r + θ / 360 × 2πr
[Arc length of a circle = θ / 360 × 2πr]

Perimeter of a sector = 2 × 2 + 90 / 360(2π × 2)
[Substitute the value of r and θ].

= 4 + π.
[Simplify]

So, perimeter of the sector is (4 + π) cm.


Correct answer : (3)
 5.  
Find the area of the sector AOB.


a.
3.25π cm2
b.
3π cm2
c.
6.75π cm2
d.
4.5 cm2


Solution:

Area of the sector of a circle = 1 / 2r2θ
[Formula.]

θ = 120° = 120 × π / 180 = 2π3 radians
[Convert degrees to radians.]

= 1 / 2 × (4.5)2 × 2π3
[Substitute the values.]

= 6.75π
[Simplify.]

So, the area of the sector of the circle is 6.75π cm2.


Correct answer : (3)
 6.  
Find the area of the sector POQ of the circle of radius 8 cm.


a.
8 cm2
b.
4 cm2
c.
8π cm2
d.
4π cm2


Solution:

Area of the sector of a circle = 1 / 2r2θ
[Formula.]

45° = 45 × π / 180 = π / 4 radians
[Convert degrees to radians.]

= 1 / 2 × (8)2 × π / 4
[Substitute the values.]

= 8π
[Simplify.]

So, the area of the sector of the circle is 8π cm2.


Correct answer : (3)
 7.  
The central angle of a sector is 30° and the radius of the circle is 6 cm. Find the area of the sector of the circle.
a.
3π2 square cm
b.
2π3 square cm
c.
3π square cm
d.
6π square cm


Solution:

Area of the sector of a circle = 1 / 2r2θ
[Formula.]

30° = 30 × π / 180 = π / 6 radians
[Convert degrees to radians.]

= 1 / 2 × (6)2 × π / 6
[Substitute the values.]

= 3π
[Simplify.]

So, the area of the sector of the circle is 3π square cm.


Correct answer : (3)
 8.  
The angle of a sector is 90 degrees and the radius of the circle is 3 cm. Calculate the area of the sector.
a.
3π2 square cm
b.
9π2 square cm
c.
9π4 square cm
d.
3π4 square cm


Solution:

Area of the sector of a circle = 1 / 2r2θ
[Formula.]

90° = 90 × π / 180 = π / 2 radians
[Convert degrees to radians.]

= 1 / 2 × (3)2 × π / 2
[Substitute the values.]

= 9π4

So, the area of the sector of the circle is 9π4 square cm.


Correct answer : (3)
 9.  
If the diameter of a circle is doubled, how is the circumference changed?
a.
multiplied by 2
b.
divided by 2
c.
divided by 4
d.
multiplied by 4


Solution:

Let, the diameter of a circle be d units.

If diameter of a circle is d units, then circumference of the circle = πd units.

If the diameter of the circle is doubled, then diameter of the new circle will be 2d units.

Circumference of the new circle = π(2d) units = 2πd units = 2 × original circumference of the circle.

Therefore, circumference of the new circle will be two times the original circumference of the circle.


Correct answer : (1)
 10.  
If the radius of a circle is multiplied by 2, how is the area changed?
a.
multiplied by 4
b.
divided by 4
c.
divided by 2
d.
multiplied by 2


Solution:

Let, the radius of a circle be r units.

If the radius of a circle is r units, then area of the circle = πr2 square units.

If the radius of the circle is multiplied by 2, then radius of the new circle will be 2r units.

Area of the new circle = π(2r)2 square units = 4πr2 square units = 4 × original area of the circle.

Therefore, area of the new circle will be four times the original area of the circle.


Correct answer : (1)

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