Perimeter and Area Test

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Perimeter and Area Test - 33

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Weekly Quiz Competition

Question 1
1 / -0

Two concentric circles form a ring. The inner and outer circumferences of the ring are $$50\dfrac{2}{7}\ m$$ and $$75\dfrac{3}{7}\ m$$ respectively. Find the width of the ring.

A
$$3\ m$$

B
$$4\ m$$

C
$$5\ m$$

D
$$6\ m$$
Question 2
1 / -0

If the base and altitude of a parallelogram are doubled, what happens to the area compared to the original one?

A
$$8$$ times original

B
$$2$$ times original

C
$$4$$ times original

D
Remains same

Solution

Area of parallelogram $$S_1=bh$$, where $$b$$ is the base and $$h$$ is the height.

New Area, $$S_2=2b\times 2h$$
$$=4bh$$
$$=4S_1$$
Hence, the area becomes $$4$$ times the original area.
Question 3
1 / -0

Find the area of a ring shaped region enclosed between two concentric circles of radii $$20$$ cm and $$15$$ cm.

A
$$175\pi cm^2$$

B
$$75\pi cm^2$$

C
$$275\pi cm^2$$

D
$$750\pi cm^2$$

Solution

We know that area of a circle is $$πr^2$$, where $$r$$ be a radius of the circle.
Let us assume $$R = 20$$ $$cm$$ & $$r = 15$$ $$cm$$
$$\therefore$$ Required area $$= \pi (R^2 - r^2 ) = \pi (20^{2} - 15^{2}) = 175π cm^{2}$$.
Question 4
1 / -0

Find the area of a parallelogram having base $$4$$ cm and height $$2$$ cm.

A
$$6$$ sq. cm

B
$$8$$ sq. cm

C
$$10$$ sq. cm

D
$$12$$ sq. cm

Solution

Base of the parallelogram, $$b=4$$ cm
Height, $$h=2$$ cm

Area of the parallelogram $$=b\times h$$

$$=4\times 2$$

$$=8$$ $$cm^{2}$$
Question 5
1 / -0

The circumference of a circle is $$31.4\ cm$$. Find the area of the circle? (Take $$\pi=3.14$$)

A
$$58.5cm^2$$

B
$$48.5cm^2$$

C
$$78.5cm^2$$

D
$$88.5cm^2$$

Solution

Given,
circumference of the circle$$ = 31.4cm$$

Let, the radius be $$r$$

$$\Rightarrow 2\pi r = 31.4$$

$$\Rightarrow r = \dfrac{31.4}{2\times \pi}$$

$$\Rightarrow r = \dfrac{31.4}{2\times 3.14}$$

$$\Rightarrow r = 5$$

So, the radius $$r=5\ cm$$

Now, Area of circle $$= \pi r^2$$

$$= 3.14\times (5)^2\ cm^2$$

$$= 3.14\times 25\ cm^2$$

$$=78.5\ cm^2$$

Hence, the area of the circle is $$78.5\ cm^2$$.
Question 6
1 / -0

Find the area of the circular park of Janakpuri whose circumference is 77m

A
$$671.87m^2$$

B
$$331.62m^2$$

C
$$471.62m^2$$

D
$$401.62m^2$$

Solution

Given that,

Circumference of a circle $$=77\,m$$

We know that,

Circumference of a circle $$=2\pi r=77$$

$$ \Rightarrow 2\times \dfrac{22}{7}\times r=77 $$

$$ \Rightarrow r=\dfrac{77\times 7}{2\times 22} $$

$$ \Rightarrow r=\dfrac{49}{4} $$

Then, Area of circular park

$$ =\pi {{r}^{2}}=\dfrac{22}{7}\times \dfrac{49}{4}\times \dfrac{49}{4} $$

$$ \Rightarrow \dfrac{11\times 7\times 49}{2\times 4} $$

$$ \Rightarrow \dfrac{77\times 49}{8} $$

$$ \Rightarrow \dfrac{3773}{8}\,\,{{m}^{2}} $$

$$ or $$

$$ \Rightarrow 471.62\,{{m}^{2}} $$
Question 7
1 / -0

Find the area of a circle whose radius is $$6$$ $$cm$$.

A
$$26$$ $$ c{m^2}$$

B
$$46$$ $$ c{m^2}$$

C
$$56$$ $$ c{m^2}$$

D
$$36$$ $$ c{m^2}$$

E
none

Solution

The radius of circle is $$6$$ $$cm$$

The area of circle is given as $$πr^2$$

$$\implies π(6)^2$$ $$cm^2$$

$$\implies 36π$$ $$cm^2$$
Question 8
1 / -0

If the perimeter of a circle is $$132$$ cm, find its area.

A
$$1356$$ sq. cm

B
$$1386$$ sq. cm

C
$$1340$$ sq. cm

D
$$1436$$ sq. cm

Solution

Let the radius of the circle is $$r$$ cm
Perimeter of a circle $$=2\pi r=132$$

$$ \Rightarrow 2\times \cfrac{22}{7}\times r=132$$

$$\Rightarrow r=\cfrac{132\times 7}{22\times 2}$$

$$\Rightarrow r=21$$ cm

Area of the circle $$=\pi r^{2}$$
$$ \Rightarrow =\cfrac{22}{7}\times 21\times 21$$
$$ \Rightarrow =1386$$ $$cm^{2}$$
Question 9
1 / -0

One diagonal of a parallelogram is $$7cm$$ and the perpendicular distance of this diagonal from either of the outlying vertices is $$27cm$$. The area of the parallelogram (in sq.cm) is:

A
$$180$$

B
$$183$$

C
$$189$$

D
$$198$$

Solution

Area of parallelogram $$=2 \times $$area of $$\triangle ACD$$
$$=2\times \dfrac{1}{2}\times 27 \times 7$$
$$189\ cm^2$$
Question 10
1 / -0

The radius of a circular wheel is $$1.75\ m$$. The number of revolutions that it will make in covering $$11\ kms$$ is:

A
$$1000$$

B
$$100000$$

C
$$100$$

D
$$10$$

Solution

Let It take 'n' revolution

Then $$ n\times 2\pi r = 11,000$$

$$\displaystyle \Rightarrow n\times2\times \frac{22}{7}\times 1.75 = 11000$$

$$\displaystyle \therefore n = 1000$$

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Re-Attempt Weekly Quiz Competition

Perimeter and Area Test - 33

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Perimeter and Area Test - 33

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SHARING IS CARING

Question 1

$$3\ m$$

$$4\ m$$

$$5\ m$$

$$6\ m$$

Question 2

$$8$$ times original

$$2$$ times original

$$4$$ times original

Remains same

Solution

Question 3

$$175\pi cm^2$$

$$75\pi cm^2$$

$$275\pi cm^2$$

$$750\pi cm^2$$

Solution

Question 4

$$6$$ sq. cm

$$8$$ sq. cm

$$10$$ sq. cm

$$12$$ sq. cm

Solution

Question 5

$$58.5cm^2$$

$$48.5cm^2$$

$$78.5cm^2$$

$$88.5cm^2$$

Solution

Question 6

$$671.87m^2$$

$$331.62m^2$$

$$471.62m^2$$

$$401.62m^2$$

Solution

Question 7

$$26$$ $$ c{m^2}$$

$$46$$ $$ c{m^2}$$

$$56$$ $$ c{m^2}$$

$$36$$ $$ c{m^2}$$

none

Solution

Question 8

$$1356$$ sq. cm

$$1386$$ sq. cm

$$1340$$ sq. cm

$$1436$$ sq. cm

Solution

Question 9

$$180$$

$$183$$

$$189$$

$$198$$

Solution

Question 10

$$1000$$

$$100000$$

$$100$$

$$10$$

Solution

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