Perimeter and Area Test

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Perimeter and Area Test - 34

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Weekly Quiz Competition

Question 1
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A race track is in the form of ring whose inner and outer circumstances are $$352\ meters$$ and $$396\ meters$$ respectively. Find the width of the track.

A
$$7\ meters$$

B
$$14\ meters $$

C
$$14\pi\ meters $$

D
$$7\pi\ meters $$

Solution

Let, $$R, r $$ be the outer and inner radius of the track then,
$$2\pi R = 396 \ m$$
$$2\pi r = 352 \ m $$

Now , $$2\pi R - 2\pi r = 396 - 352$$

$$\implies 2\pi (R - r) = 44 $$

$$\implies 2\times \dfrac{22}{7} \times (R - r) = 44 $$

$$\implies R - r = 44 \times \dfrac{7}{44}$$

$$\therefore R - r = 7 \ m $$

i.e., The width of the track $$ = 7 \ m $$

Option A is correct.
Question 2
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If the area of a parallelogram is $$144 \operatorname { cm } ^ { 2 }$$ and its base is $$9 cm$$. then its height is

A
$$8 cm$$

B
$$12 cm$$

C
$$24 cm$$

D
$$16 cm$$

Solution

Area of parallelogram $$= $$ base$$\times$$ height

Given : base $$=9\ cm,$$
area $$=144\ cm^2$$
Let height be $$h$$

$$\Rightarrow$$ $$144\ {cm}^{2}=9cm\times h$$

$$\Rightarrow$$ $$h$$$$=\cfrac{144\ {cm}^{2}}{9\ cm}$$

$$\therefore$$ $$h=16\ cm$$
Question 3
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If the circumference of a circle is 88 cm, then the area of a circle (in sq. cm) is:

A
$$196\pi $$

B
$$92\pi $$

C
$$64\pi $$

D
$$48\pi $$

Solution

Given,

Circumference of the circle,

$$2\pi r=88$$

$$\therefore r=\dfrac{44}{\pi}=14$$

Area of circle,

$$A=\pi r^2$$

$$=\pi \times 14^2$$

$$=196 \pi$$
Question 4
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The area of a circle whose diameter is 1.4 cm is

A
$$1.54\ cm^2 $$

B
$$0.77\ cm^2 $$

C
$$6.16\ cm^2 $$

D
None of these

Solution

Area of cirlce

$$=\pi r^2$$

$$=\pi \left ( \dfrac{d}{2} \right )^2$$

$$=\dfrac{22}{7} \left ( \dfrac{1.4}{2} \right )^2$$

$$=1.54m^2$$
Question 5
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Find the circumference of the circles with the radius 14cm :$$(Take \ \pi = \frac{22}{7})$$

A
88 cm

B
28 mm

C
21 cm

D
90 cm

Solution

Circumference $$ = 2\pi r $$
$$ r = 14 \,cm $$
$$ = 2\pi r = 2\times \frac{22}{7}\times 14 $$
$$ = 2\times 22\times 2 $$
$$ = 4\times 22 $$
$$ = 88 \,cm $$
Question 6
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An ant is moving around a few food pieces of different shapes scattered on the floor. For which food-piece would the ant have to take a longer round? Remember, circumference of a circle can be obtained by using the expression $$c =2\pi r$$, where r is the radius of the circle.

A

B

C

D
$$ None\ of\ these$$

Solution

$$(a)$$Diameter$$=2.8$$cm$$\Rightarrow$$Radius$$=\dfrac{2.8}{2}=1.4$$cm
Perimeter of a circle$$=2\pi r\Rightarrow $$ Perimeter of a semicircle$$=\dfrac{2\pi r}{2}=\pi r$$
$$\therefore$$ Perimeter of the figure$$=\pi r+$$ diameter
$$=\dfrac{22}{7}\times\dfrac{14}{10}+2.8$$cm
$$=4.4+2.8=7.2$$cm

$$(b)$$Perimeter of the semi-circular part$$=\pi r$$
$$=\dfrac{22}{7}\times 1.4$$cm
$$=4.4$$cm
Perimeter of the remaining part$$=1.5+2.8+1.5=5.8$$cm
Total perimeter$$=4.4+5.8=10.2$$

$$(c)$$Perimeter of the semi-circular part$$=\dfrac{\pi d}{2}=\dfrac{22}{7}\times \dfrac{2.8}{2}=4.4$$cm
$$\therefore$$ Perimeter of the figure$$=4.4+2+2=8.4$$cm
Since,$$7.2$$cm$$<8.4$$cm$$<10.2$$cm
$$\therefore$$ perimeter of figure $$b$$ has the longest round.
Question 7
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Find the area of circle whose circumference is $$220cm$$

A
3850

B
3500

C
3700

D
3900

Solution

Circumference of circle $$=220\,cm$$ [ Given ]
Circumference of circle $$=2\pi r$$
$$\Rightarrow$$ $$220=2\times\dfrac{22}{7}\times r$$

$$\Rightarrow$$ $$r=220\times \dfrac{7}{22}\times\dfrac{1}{2}$$

$$\Rightarrow$$ $$r=5\times 7$$

$$\therefore$$ $$r=35\,cm^2$$

$$\Rightarrow$$ Area of circle $$=\pi r^2$$

$$=\dfrac{22}{7}\times 35\times 35$$

$$=22\times 5\times 35$$

$$=3850\,cm^2$$
Question 8
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The area of parallelogram if the base is $$36cm$$ and height is $$45cm$$

A
1620

B
1800

C
1250

D
1640

Solution

The base of parallelogram is $$36cm$$
The height is $$45cm$$
The area of parallelogram is $$36\times 45=1620cm^2$$
Question 9
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The area of the concentric circles are $$962.5\ cm^{2}$$ and $$1368\ cm^{2}$$. Find the width of the ring formed by them.

A
$$2.1\ cm$$

B
$$1 cm$$

C
$$5.5\ cm$$

D
$$3.5\ cm$$

Solution

Let the radii of the bigger and smaller circles be $$R\space\mathrm{cm}$$ and $$r \space\mathrm{cm}$$, respectively.
Now, Area of the bigger circle $$=\pi R^2$$
$$\Rightarrow 1386=\frac{22}{7}\times R^2$$
$$\Rightarrow R^2=\frac{1386\times7}{22}$$
$$\Rightarrow R^2=441$$
$$\Rightarrow R=21$$
$$\therefore$$ Radius of bigger circle $$(R)=21\space\mathrm{cm}$$
Similarly, Area of the smaller circle $$=\pi r^2$$
$$\Rightarrow 962.5=\frac{22}{7}\times r^2$$
$$\Rightarrow r^2=\frac{962.5\times7}{22}$$
$$\Rightarrow r^2=306.25$$
$$\Rightarrow r=17.5$$
$$\therefore$$ Radius of smaller circle $$(r)=17.5\space\mathrm{cm}$$
Hence, Width of Ring $$= R-r=21-17.5=3.5\space\mathrm{cm}$$
Thus, $$\text{D}$$ is the correct option.
Question 10
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Find the radius of circle if its area is $$125\pi cm^2$$

A
$$5\sqrt 5cm$$

B
$$3\sqrt 3cm$$

C
$$2\sqrt 2cm$$

D
none

Solution

The area of circle is $$125\pi cm^2$$
The area of circle of radius $$ r =\pi r^2$$
$$\therefore 125\pi cm^2= πr^2 $$
$$ r^2=125$$
$$\Rightarrow r=5\sqrt 5cm$$