MCQ Questions for Class 7 Maths Perimeter And Area Quiz 1

The area of a circle is the measurement of the region enclosed by its

0%
Radius
0%
Centre
0%
Circumference
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Area

Circumference of a circle is .....................

0%
$\pi r$
0%
$2\pi r$
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$3\pi r$
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$4\pi r$

Explanation

Circumference of a circle whose radius is

$r$ is given by

$2\pi r.$

Calculate the radius of a circle whose circumference is

$44\ cm$ ?

0%
$7\ cm$ .
0%
$14\ cm$ .
0%
$21\ cm$ .
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None of these

Explanation

Given: Circumference of circle

$=44\space\mathrm{cm}$

$\Rightarrow 2\pi r=44$

$\Rightarrow 2\times\dfrac{22}{7}\times r=44$

$\Rightarrow r=44\times\dfrac{1}{2}\times\cfrac{7}{22}$

$\Rightarrow r=7\space\mathrm{cm}$

$\therefore$ Radius of circle

$r=7\space\mathrm{cm}$

Hence,

$\text{A}$ is the correct option.

Consider the railway platform which is in square shape having side length

$2\ km$ . Then area of the platform is

$4$ ____.

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$m$
0%
$km$
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$km^{2}$
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$m^{2}$

Explanation

Area of square platform

$=2\times 2=4 km^2$

Circumference of a circle is always

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more than three times of its diameter
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three times of its diameter
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less than three times of its diameter
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three times of its radius.

Explanation

Option (a) is correct.
As we know [bat Circumference of a circle

$2 \times 3.14 \times r$

$\Rightarrow circumference = 3.14 \times d$
Therefore, Circumference of a circle is more than three of its diameter.

State true or false.

The area of a circle whose radius is

$2.1$ m is

$13.86\,\, m^2$

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True
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False

Explanation

Area of a circle with radius

$r$ is

$\pi {r}^{2}$
Area of circle of radius

$2.1 \text{ m}$

$= \pi { r }^{ 2 }$

$= \dfrac { 22 }{ 7 } \times 2.1\times 2.1$

$=13.86\text{ m}^{ 2 }$

Area of a circle is ...................

0%
$\pi r^2$
0%
$2\pi r$
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$2\pi r^2$
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$4\pi r$

Explanation

Area covered within the boundary of circle =

$\pi \times r^2$ , where

$r$ is a radius of a circle.

What is the area of the circular ring included between two concentric circles of radius

$14$ cm and

$10.5$ cm ?

0%
$255\ cm^2$
0%
$148\ cm^2$
0%
$324\ cm^2$
0%
$269\ cm^2$

Explanation

Let

$R$ be the radius of the larger circle
Hence

$R=14\ cm$

Let

$r$ be the radius of the smaller circle
Hence

$r=10.5\ cm$

Area of the circular ring

$=$ Area of the larger circle - Area of the smaller circle

$=\pi R^2 - \pi r^2$

$=\dfrac { 22 }{ 7 } \times \left( { R }^{ 2 } - { r }^{ 2 } \right)$

$= \dfrac { 22 }{ 7 } \times \left( { 14 }^{ 2 } - { 10.5 }^{ 2 } \right)$

$=269.5 \ { cm }^{ 2 }$

$\approx 269\ { cm }^{ 2 }$

In Fig. 9.4, the area of parallelogram ABCD is :

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AD x BM
0%
BC x BN
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DC x DL
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AD x DL

Explanation

$Given-\\ ABCD\quad is\quad a\quad parallelogram.\quad \\ DL\bot AB\quad \& \quad BM\bot AD.\quad \\ To\quad find\quad out-\quad arABCD.\\ Solution-\\ DL\bot AB\quad \therefore \quad DL\quad is\quad the\quad height\quad of\quad ABCD\quad when\quad its\quad base\quad is\quad AB.\\ \therefore \quad arABCD=DL\times AB..\\ Similarly\quad BM\bot AD.\\ \therefore \quad BM\quad is\quad the\quad height\quad of\quad ABCD\quad when\quad its\quad base\quad is\quad AD.\\ \therefore \quad arABCD=BM\times AD\\ Ans-\quad Option\quad A\quad \& \quad C$

One side of a parallelogram is

$8$ cm. If the corresponding altitude is

$6$ cm, then its area is given by

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$24\: cm^2$
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$36\: cm^2$
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$40\: cm^2$
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$48\: cm^2$

Explanation

Area of parallelogram

$=$ length

$\times$ height
Here altitude is nothing but the height

$\therefore$ Area of parallelogram

$= 8 \times 6$

$= 48\: cm^2$

A path of width 8 m runs around a circular park whose radius is

$38\ m$ . Find the area of the path.

0%
$2112\ m^2$
0%
$2834\ m^2$
0%
$3212\ m^2$
0%
$1578\ m^2$

Explanation

Inner radius (Radius of the park)

$=38\ m$
Outer radius (Radius of the park

$+$ path width of the park)

$=38+8=46\ m$
Area of the path

$=\pi(46^2-38^2)$

$=\cfrac{22}{7}(2116-1444)$

$=\cfrac{22}{7}(672)$

$=2112\ m^2$

In the given figure, the area enclosed between two concentric circles is

$808.5\ cm^2$ . The circumference of the outer circle is

$242\ cm$ . Find the width of the ring.

0%
$1.2\ cm$
0%
$2.4\ cm$
0%
$3.5\ cm$
0%
$4.2\ cm$

Explanation

Let radius of the inner circle be

$r$ and radius of the outer circle be

$R$
Area enclosed between the two concentric circles

$=\pi(R^2-r^2)$
Given

$2\pi R=242$

$\Rightarrow R=\cfrac{242 \times 7}{22\times 2}$

$\Rightarrow R=\cfrac{77}{2}$
Now,

$\pi(R^2-r^2)=808.5$

$\Rightarrow {\left(\cfrac{77}{2}\right)}^2-r^2=\cfrac{808.5 \times 7}{22}$

$\Rightarrow \cfrac{5929}{4}-r^2=257.25$

$\Rightarrow r^2=1225$

$\Rightarrow r=35$
Radius of the inner circle

$=35\ cm$

$\therefore$ width of the ring

$=(R-r)$

$=(38.5-35)\ cm$

$=3.5\ cm$

The circumference of a circular field is

$528\ m$ . Then its area is

0%
22176 $m^2$
0%
26400 $m^2$
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10080 $m^2$
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84000 $m^2$

Explanation

$Given-\\ the\quad circumference=C\quad of\quad a\quad circular\quad field=528m.\\ To\quad find\quad out-\\ the\quad ar.circle=?\\ Solution-\\ Let\quad the\quad radius\quad of\quad the\quad circle\quad be\quad r.\\ Then\quad r=\cfrac { C }{ 2\pi } \quad when\quad C=circumference\quad of\quad the\quad circle.\\ \Longrightarrow r=\cfrac { 528 }{ 2\times \cfrac { 22 }{ 7 } } cm=84m.\\ \therefore \quad ar.circle=\pi { r }^{ 2 }=\cfrac { 22 }{ 7 } \times { 84 }^{ 2 }{ m }^{ 2 }=22176{ m }^{ 2 }.\\ Ans-\quad Option\quad A.$

The radius of a circle is

$5\: m$ . Find the circumference of the circle whose area is

$49$ times the area of the given circle.

0%
$220 \: m$
0%
$120 \: m$
0%
$320 \: m$
0%
$420 \: m$

Explanation

Radius of given circle

$=5\ m$

Therefore,

Area of given circle

$=\pi R^2=\pi (5)^2$

$=25\pi\ m^2$

Let radius of required circle

$=r$

Therefore, According to the given condition,

$\pi r^2=49\times 25\pi$

$\Rightarrow r^2=(7\times 5)^2$

$\Rightarrow r=35m$

Therefore,

Circumference

$=2\pi r$

$=2\times \dfrac { 22 }{ 7 }\times35$

$=220\ m$

Find the area of a ring whose outer and inner radii are

$19\ cm$ and

$16\ cm$ respectively.

0%
$330\ cm^2$
0%
$310\ cm^2$
0%
$320\ cm^2$
0%
$350\ cm^2$

Explanation

Let us given

$R = 19$

$cm$ &

$r = 16$

$cm$

Area of outer circle

$=\pi{(19)}^2$

$=\cfrac{22}{7}\times 361$
Area of inner circle

$=\pi{(16)}^2$

$=\cfrac{22}{7}\times 256$

$\therefore$ area of the ring

$=\dfrac{22}{7}\times 361-\dfrac{22}{7}\times 256$

$=\cfrac{22}{7}(361-256)$

$=\cfrac{22}{7}(105)$

$=330\ cm^2$

The circumference of a circular field is

$308 m$ . Find its radius in metres.

0%
$49$ m
0%
$59$ m
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$91$ m
0%
$94$ m

Explanation

The circumference of a circular field is

$308m$
Therefore,

$2\pi r=308$

$\Rightarrow r=\cfrac{308\times 7}{2\times 22}$

$\Rightarrow r=49m$

The total boundary length of circle is called

0%
area
0%
volume
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circumference
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diameter

A circle is inscribed in a square as shown below. If the radius of the circle is

$4$ cm, then the perimeter of the square is ______

0%
$28$ cm
0%
$24$ cm
0%
$32$ cm
0%
$36$ cm

Explanation

From the fig it is clear that,

Diameter of the circle

$=$ side of the square
So length of side of square

$=2\times$

$4$ cm

$=8$ cm

$\therefore$ perimeter of the square

$=8 + 8 + 8 + 8$

$= 32$ cm

Find the missing length of the following figure.

0%
$6\text{ cm}$
0%
$4\text{ cm}$
0%
$2\text{ cm}$
0%
$5\text{ cm}$

Explanation

Let unknown side of the figure is

$x$

Perimeter

$=$ sum of all sides of figure

$23=4+5+8+x$

$x=23-17=6\text{ cm}$ .

Find the missing length of the figure given below.

0%
$4\text{ cm}$
0%
$2\text{ cm}$
0%
$6\text{ cm}$
0%
$8\text{ cm}$

Explanation

Let unknown side is

$x$

Perimeter

$=$ sum of length.

$20=6+4+8+x$

$x=20-18=2\text{ cm}$

Perimeter of a circle is called as__________

0%
Area
0%
Circumference
0%
Volume
0%
None of these

Explanation

Perimeter of a circle is equal to its circumference i.e.,

$P=2\pi r$

Perimeter of a circle is called its

0%
radius
0%
area
0%
diameter
0%
none of these

Perimeter of a circle is called as

0%
area
0%
circumference
0%
volume
0%
none of these

Explanation

Perimeter of a circle is called as circumference.
The formula of circumference is

$2\pi r$
Option B is correct.

Perimeter of a triangle is the sum of the lengths of all the ............ sides.

0%
$4$
0%
$2$
0%
$3$
0%
$6$

The radius of a wheel is

$0.25 m$ . How many rounds will it take to complete the distance of

$11 km$ ?

0%
$7000$
0%
$8000$
0%
$9000$
0%
$6000$

Explanation

Distance covered in one round

$=$ Circumference of wheel

$\Rightarrow 2\pi r= 2 \times \cfrac{22}{7} \times 0.25 =\cfrac{11}{7}m$

$\displaystyle \therefore$ Number of rounds to cover

$11 km =\cfrac{\text {Total distance covered}}{\text {Distance covered in one round}}=\cfrac{11\times\:1000}{\frac{11}{7}}=7000$

What is the area of the given figure?

$ABCD$ is a rectangle and

$BDE$ is an isosceles right triangle.

0%
$ab$
0%
$\displaystyle ab^{2}$
0%
$cab$
0%
$b\left(a + \dfrac b2\right)$

If the radii of two concentric circles are

$15\ \text{cm}$ and

$13\ \text{cm}$ , respectively, then the area of the circulating ring in sq. cm will be:

0%
$176$
0%
$178$
0%
$180$
0%
$200$

Explanation

$R = 15\ \text{cm}, r = 13\ \text{cm}.$

Area of the circulating ring

$= \pi (R^2-r^2)$

$= \cfrac {22}{7} ({15}^2-{13}^2)\ \text{cm}^2$

$= \cfrac {22}{7} \times 28 \times 2\ \text{cm}^2$

$=176\ \text{cm}^2$

The diameter of each circle shown in the given figure is 'd' then the area of the square is given by

0%
$9\displaystyle d^{2}$
0%
$9 d$
0%
$3\displaystyle d^{2}$
0%
$\displaystyle \frac{3}{4} d^{2}$
0%
$\displaystyle \frac{4}{3} d^{2}$

Explanation

There are 3 circles of diameter 'd

So side of the square is 3d and

Hence area is

$side^2=\displaystyle 9d^{2}$

The area of a circle is 301.84

$\displaystyle cm^{2}$ Then its radius is

0%
$9.2$ cm
0%
$9.3$ cm
0%
$9.8$ cm
0%
9.6 cm

Explanation

Area of the circle =

$\displaystyle \pi r^{2}$
According to the question,

$\displaystyle \pi r^{2}=301.84$

$\displaystyle \Rightarrow \frac{22}{7}r^{2}=301.84$

$\displaystyle r^{2}=\frac{7\times 301.84}{22}=96.04$

$\displaystyle \therefore r=\sqrt{96.04}=9.8\ cm$

A circular park has a path of uniform width around it. The difference between the outer and inner circumferences of the circular park is

$132$ m. Its width is

0%
$20$ m
0%
$21$ m
0%
$22$ m
0%
$24$ m

Explanation

Let

$r_1$ and

$C_1$ be the radius and the circumference of the inner circle.

Let

$r_2$ and

$C_2$ be the radius and the circumference of the outer circle.

The width of the circular path is

$(r_2-r_1)$ m.

Given,

$C_2-C_1=132$ m

$\Rightarrow 2\pi r_2 - 2\pi r_1=132$

$\Rightarrow 2\pi (r_2-r_1)=132$

$\Rightarrow r_2-r_1=\cfrac{66}{\dfrac{22}{7}}$

$\Rightarrow r_2-r_1=21$

Thus, width of the circular path is

$21$ m.

CBSE Questions for Class 7 Maths Perimeter And Area Quiz 1 - MCQExams.com

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Practice Class 7 Maths Quiz Questions and Answers

CBSE Questions for Class 7 Maths Perimeter And Area Quiz 1 - MCQExams.com

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Practice Class 7 Maths Quiz Questions and Answers

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