Perimeter and Area Test

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Perimeter and Area Test - 12

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Weekly Quiz Competition

Question 1
1 / -0

The difference in the area of a square of perimeter $$88$$ m and a circle with same circumference is

A
166 $$\displaystyle cm^{2}$$

B
122 $$\displaystyle cm^{2}$$

C
133 $$\displaystyle cm^{2}$$

D
132 $$\displaystyle cm^{2}$$

Solution

Perimeter of $$sq=88 cm$$
$$\displaystyle \therefore $$ side of $$sq = 22 cm$$
$$\displaystyle \Rightarrow $$ area of sq $$\displaystyle =484 cm^{2}$$
$$\displaystyle C=2\pi r=88\Rightarrow r=14$$
$$\displaystyle \therefore Area=\dfrac{22}{7}\times 14\times 14=616cm^{2}$$
Difference in the areas $$\displaystyle =616-484=132 cm^{2}$$
Question 2
1 / -0

The ratio of the outer and inner circumferences of a circular path is $$23:22$$, If the path is $$5\ m$$ wide, the radius of the inner circle is:

A
$$55\ m$$

B
$$110\ m$$

C
$$220\ m$$

D
$$230\ m$$

Solution

Let R and r be the outer and inner radii of the circular path.
Given that,
$$\frac{2\pi R}{2\pi r}=\frac{23}{22}$$
$$=>\frac{R}{r}=\frac{23}{22}$$
Let $$R=23x$$ and $$r=22x$$
It is given that the width of the path is $$5$$m wide
$$\therefore R-r=5$$m
$$=>23x-22x=5$$
$$=>x=5$$
$$\therefore$$ the inner radius of the circle is
$$=22\times 5$$
$$=110$$m
Question 3
1 / -0

The radius of a circle whose area is equal to the sum of the areas of two circles of radii 3 cm and 4 cm is

A
5 cm

B
5.5 cm

C
5.8 cm

D
6 cm

Solution

The area of circle $$C_1$$ whose radius is $$4\ cm =\pi (4)^{2}$$

$$=16\pi $$ sq cm

And the area of circle $$C_2$$ whose radius is $$3\ cm = \pi (3)^{2}$$

$$=9\pi $$ sq cm

Given: Area of the new circle is equal to the sum of areas of circles $$C_1$$ and $$C_2$$

Let the radius of the new circle be $$R$$ cm

Area of big circle $$=16\pi +9\pi =25\pi $$ sq cm

$$\Rightarrow$$ $$\pi R^{2}=25\pi$$

$$ \Rightarrow$$ $$R^{2}=25$$

$$\Rightarrow$$ $$R=5$$ cm

So the radius of the new circle $$=5$$ cm
Question 4
1 / -0

Area of a square 625 sq m. Then the measure of its side is

A
$$15$$ m

B
$$25$$ m

C
$$20$$ m

D
$$24$$ m

Solution

We know that,
Area$$=side\times side$$
$$s \displaystyle \times s \displaystyle= 625 \displaystyle m^{2} $$
$$ s \displaystyle \times s \displaystyle = 25 \displaystyle \times 25$$ $$\displaystyle= $$ 625 $$\displaystyle m^{2} $$
$$s \displaystyle = 25\ m$$
Question 5
1 / -0

The radius of a circle whose area is equal to the sum of the areas of two circles of radii are 5 cm and 12 cm is

A
13 cm

B
14 cm

C
15 cm

D
none

Solution

Given two circle radii are $$5 cm$$ and $$12 cm$$
Then,
Area of circle of radius 5 cm $$=$$$$\pi r^{2}=\pi (5)^{2}=25\pi $$ sq cm
Area of circle of radius 12 cm $$=$$$$\pi r^{2}=\pi (12)^{2}=144\pi $$sq cm
So area of circle whose area is equal to sum of areas of two circles$$=$$$$25\pi +144\pi =169\pi $$ sq cm
Let the radius of the bigger circle be $$=$$R cm
$$\therefore \pi R^{2}=169\pi$$
$$\Rightarrow R^{2}=169$$
$$\Rightarrow R=13 cm$$
Question 6
1 / -0

Find the perimeter of a circle whose radius is 7 cm (in cm)

A
$$\displaystyle 12\pi $$

B
$$\displaystyle 14\pi $$

C
$$\displaystyle 16\pi $$

D
$$\displaystyle 10\pi $$

Solution

Perimeter of a circle $$ = 2\pi r $$, where r is the radius of the circle

So, perimeter of the given circle $$ = 2 \times \pi \times 7 = 14 \pi $$
Question 7
1 / -0

If the area of the circle be $$ \displaystyle 154 \text{ cm}^{2},$$ then its radius is equal to:

A
$$12\text{ cm}$$

B
$$8\text{ cm}$$

C
$$7\text{ cm}$$

D
None of these

Solution

Area of the circle $$=154\displaystyle \text{ cm}^{2}$$
$$\because $$ Area $$=\displaystyle \pi r^{2}$$
$$\therefore \pi r^2=154$$
$$\Rightarrow$$ $$\displaystyle r^{2}=\frac{154\times 7}{22}$$
$$ \Rightarrow r^2 = \displaystyle 7\times 7$$
$$\displaystyle \Rightarrow r=7\text{ cm}$$
Question 8
1 / -0

If the circumference of a circle be $$8.8 \text{ m}$$ then its radius is equal to -

A
$$1.60 \text{ m}$$ (approx)

B
$$1.61 \text{ m}$$ (approx)

C
$$1.40 \text{ m}$$ (approx)

D
None of these

Solution

Circumference of a circle, $$\displaystyle C=2\pi r $$
or $$\displaystyle r=\frac{C}{2\pi } $$
$$=\displaystyle \frac{8.8\times 7}{2\times 22} $$ $$= 1.4 \text{ m}$$
Question 9
1 / -0

If the radius of a circle be $$r$$ $$ cm$$, then its area will be equal to-

A
$$ \displaystyle 2\pi r^{2}cm^{2} $$

B
$$ \displaystyle \pi r^{2}cm^2 $$

C
$$ \displaystyle 2\pi rcm^{2} $$

D
None of these

Solution

If radius is $$r $$ $$cm$$, then $$area=\pi r^2\,\, cm^2 $$.
Option B is correct.
Question 10
1 / -0

What is the circumference of a circle whose radius is 8 cm?

A
$$ \displaystyle 8 \pi $$

B
$$ \displaystyle 16\pi $$

C
$$ \displaystyle 61 \pi $$

D
$$ \displaystyle 24 \pi $$

Solution

Circumference=$$\displaystyle 2\pi r$$
=$$\displaystyle 2\times \pi \times 8$$
=16$$\displaystyle \pi $$ cm

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Re-Attempt Weekly Quiz Competition

Perimeter and Area Test - 12

Result

Perimeter and Area Test - 12

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SHARING IS CARING

Question 1

166 $$\displaystyle cm^{2}$$

122 $$\displaystyle cm^{2}$$

133 $$\displaystyle cm^{2}$$

132 $$\displaystyle cm^{2}$$

Solution

Question 2

$$55\ m$$

$$110\ m$$

$$220\ m$$

$$230\ m$$

Solution

Question 3

5 cm

5.5 cm

5.8 cm

6 cm

Solution

Question 4

$$15$$ m

$$25$$ m

$$20$$ m

$$24$$ m

Solution

Question 5

13 cm

14 cm

15 cm

none

Solution

Question 6

$$\displaystyle 12\pi $$

$$\displaystyle 14\pi $$

$$\displaystyle 16\pi $$

$$\displaystyle 10\pi $$

Solution

Question 7

$$12\text{ cm}$$

$$8\text{ cm}$$

$$7\text{ cm}$$

None of these

Solution

Question 8

$$1.60 \text{ m}$$ (approx)

$$1.61 \text{ m}$$ (approx)

$$1.40 \text{ m}$$ (approx)

None of these

Solution

Question 9

$$ \displaystyle 2\pi r^{2}cm^{2} $$

$$ \displaystyle \pi r^{2}cm^2 $$

$$ \displaystyle 2\pi rcm^{2} $$

None of these

Solution

Question 10

$$ \displaystyle 8 \pi $$

$$ \displaystyle 16\pi $$

$$ \displaystyle 61 \pi $$

$$ \displaystyle 24 \pi $$

Solution

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