Perimeter and Area Test

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Perimeter and Area Test - 16

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Question 1
1 / -0

If the circumference of a circle is $$352$$ metres, then its area (approx)in $$\text{ m }^{ 2 }$$ is

A
$$9859$$

B
$$8956$$

C
$$6589$$

D
$$5986$$

Solution
Question 2
1 / -0

Find the circumference of the circle with the following radius : 10 cm

A
$$20 \pi \ cm$$

B
$$10 \pi \ cm$$

C
$$30 \pi \ cm$$

D
None of these

Solution

Radius, r = 10 cm
We know, Circumference = $$2\pi r = 2 \times \pi \times 10 =20 \pi \ cm$$
Question 3
1 / -0

The area of circle with radius $$24\ cm$$ is

A
$$576\pi $$

B
$$24\pi$$

C
$$12\pi$$

D
$$48\pi$$

Solution

The radius of circle = $$24\ cm$$
The area of circle of radius $$r = \pi r^2$$
$$\therefore $$ Required area = $$π \times {24}^2\ cm^2 = 576 \pi\ cm^2$$
Question 4
1 / -0

Circumference of a circle is always

A
more than three times of its diameter

B
three times of its diameter

C
less than three times of its diameter

D
three times of its radius.

Solution

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.
Question 5
1 / -0

If the radius of a circle is tripled, The area becomes

A
$$9\ times$$

B
$$3\ times$$

C
$$remains\ the\ same$$

D
$$\sqrt{3}\ times$$

Solution

Let the radius of the circle be $$r$$.
So Area $$=A=\pi r^2$$
If radius is tripled, then radius becomes $$3r$$.

Now, area of circle $$A'=\pi(3r)^2 =9\pi r^2=9A$$
Therefore. if the radius of a circle is tripled, the area becomes $$9\ times$$.
Question 6
1 / -0

Circumference of a circle disc is $$88\, cm$$. Its radius is.

A
$$8\, cm$$

B
$$11\, cm$$

C
$$14\, cm$$

D
$$44\, cm$$

Solution

Option (c) is correct.
We know that.
Circumference $$= 2\pi r =88$$
$$\Rightarrow 88=2\times \dfrac {22}{7} \times r$$

$$\Rightarrow r=\dfrac {88\times 7}{2\times 22}$$

$$\Rightarrow r= 14\, cm$$
Therefore, $$14\,cm$$ is the radius.
Question 7
1 / -0

If $$1m^2 = x\, mm^2$$, then the value of x is.

A
$$1000 $$

B
$$10000$$

C
$$100000 $$

D
$$1000000 $$

Solution

We know that $$1m = 1000mm$$, then $$1m^2 = (1000)^2 mm$$
Option (d) is correct.
Given, $$1\,m^2= x\, mm^2$$
$$\Rightarrow (1000\,mm)^2 = x\,mm ^2$$
$$\Rightarrow x =1000000$$
Question 8
1 / -0

Area of a circle with diameter $$m$$, radius $$n$$ and circumference $$p$$ is

A
$$2 \pi \, n$$

B
$$\pi \, m^2$$

C
$$\pi \, p^2$$

D
$$\pi \, n^2$$

Solution

Option (d) is correct.
Given,
Diameter $$= m$$
Radius $$= n$$,
Circumference $$= p$$.
Therefore, area of circle $$= \pi r^2=\pi n^2$$
Question 9
1 / -0

Circumference of a circle of diameter $$5 \, cm$$ is

A
$$5 \, cm$$

B
$$ 31.4 \, cm$$

C
$$15.7 \, cm$$

D
$$1.57 \, cm$$

Solution

Option (c) is correct. Given,
Diameter $$= 5 \,cm$$
Hence. Radius $$=\dfrac {5}{2}\, cm$$

Now. circumference $$ = 2\pi r = 2\times \dfrac {22}{7}\times \dfrac {5}{2}$$
$$=\dfrac {110}{7}= 15.7\, cm$$
Question 10
1 / -0

If the sum of the areas of two circles with radii $$R_1$$ and $$R_2$$ is equal to the area of a circle of radius R, then

A
$$R_{1}+R_{2}=R$$

B
$$R_{1}^{2}+R_{2}^{2}=R^{2}$$

C
$$R_{1}+R_{2} < R$$

D
$$R_{1}^{2}+R_{2}^{2} < R^{2}$$

Solution

$$ ar.circle\quad with\quad radius\quad { R }_{ 1 }=\pi { { R }_{ 1 } }^{ 2 }\quad and\\ ar.circle\quad with\quad radius\quad { R }_{ 2 }=\pi { { R }_{ 2 } }^{ 2 }.\\ \therefore \quad sum\quad of\quad the\quad areas=\pi \left( { { R }_{ 1 } }^{ 2 }+{ { R }_{ 2 } }^{ 2 } \right) .\\ \quad Again\quad ar.circle\quad with\quad radius\quad R=\pi { { R } }^{ 2 }.\\ \therefore \quad By\quad the\quad given\quad condition\quad \pi \left( { { R }_{ 1 } }^{ 2 }+{ { R }_{ 2 } }^{ 2 } \right) =\pi { { R } }^{ 2 }\\ \Longrightarrow \left( { { R }_{ 1 } }^{ 2 }+{ { R }_{ 2 } }^{ 2 } \right) ={ { R } }^{ 2 }.\\ Ans-\quad Option\quad B.\\ $$

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Perimeter and Area Test - 16

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Perimeter and Area Test - 16

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SHARING IS CARING

Question 1

$$9859$$

$$8956$$

$$6589$$

$$5986$$

Solution

Question 2

$$20 \pi \ cm$$

$$10 \pi \ cm$$

$$30 \pi \ cm$$

None of these

Solution

Question 3

$$576\pi $$

$$24\pi$$

$$12\pi$$

$$48\pi$$

Solution

Question 4

more than three times of its diameter

three times of its diameter

less than three times of its diameter

three times of its radius.

Solution

Question 5

$$9\ times$$

$$3\ times$$

$$remains\ the\ same$$

$$\sqrt{3}\ times$$

Solution

Question 6

$$8\, cm$$

$$11\, cm$$

$$14\, cm$$

$$44\, cm$$

Solution

Question 7

$$1000 $$

$$10000$$

$$100000 $$

$$1000000 $$

Solution

Question 8

$$2 \pi \, n$$

$$\pi \, m^2$$

$$\pi \, p^2$$

$$\pi \, n^2$$

Solution

Question 9

$$5 \, cm$$

$$ 31.4 \, cm$$

$$15.7 \, cm$$

$$1.57 \, cm$$

Solution

Question 10

$$R_{1}+R_{2}=R$$

$$R_{1}^{2}+R_{2}^{2}=R^{2}$$

$$R_{1}+R_{2} < R$$

$$R_{1}^{2}+R_{2}^{2} < R^{2}$$

Solution

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