Mensuration Test

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Mensuration Test - 11

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Weekly Quiz Competition

Question 1
1 / -0

A playground which is $$ 250$$ m long and $$20$$ m broad is to be fenced with wire. How much wire is needed?

A
$$270\ m$$

B
$$230\ m$$

C
$$540\ m$$

D
None

Solution

Given that, a playground which is $$250\ m$$ long and $$20\ m$$ wide is fenced with wire.
To find out: The amount of wire.

Amount of wire needed $$=$$ Perimeter of a rectangle = $$2 \times (length+breadth)$$
Hence, wire needed $$=$$ $$2 \times(250+20)$$
$$=$$ $$540 \ m$$

Hence, the amount of wire required to fence the playground is $$540\ m$$.
Question 2
1 / -0

A man purchased a plot which is in the shape of a square The area of the plot is$$ 12$$ hectares and $$3201 m^{2}$$ Find the length of each side of the plot (in cm).

A
34900

B
35100

C
35900

D
36100

Solution

area of square plot =$$123201\ m^2$$
area=$$ (Side)^2$$
A=$$(Side)^2=123201m^2$$
$$S^2=123201$$
$$S=\sqrt { 123201 } =\sqrt { 9\times 9\times 3\times 3\times 13\times 13 } $$
S= $$9\times 3\times 13m=351m$$
S= $$35100$$cm
Answer (B) $$35100$$ cm
Question 3
1 / -0

Length and breadth of a rectangle are 3.2 m and 150 cm. Then the area is

A
$$64 sq. \ m$$

B
$$5.6 sq. \ m$$

C
$$4.8 sq. \ m$$

D
$$48 sq. \ cm$$

Solution

We know that, area of rectangle $$=l \times b$$, where $$l$$ = length, $$b $$= breadth
$$l \displaystyle = 3.2m$$
$$b \displaystyle = 1.5m$$
$$ \therefore l \displaystyle \times b\displaystyle = 3.2 \displaystyle \times 1.5$$ $$\displaystyle = 4.80$$ sq m.
Question 4
1 / -0

A hall-room $$39$$ m $$10$$ cm long and $$35$$ m $$70$$ cm broad is to be paved with equal square tiles. Find the number of tiles required, so that the tiles exactly fit.

A
$$480$$

B
$$483$$

C
$$467$$

D
$$487$$

Solution

We convert the measurements to cm

Length $$= 39 m 10cm = 3910 cm$$
Width $$= 35 m 70 cm = 3570 cm$$

To get the length of the sides of the square tile, we find the Greatest Common Divisor of $$3910$$ and $$3570$$

The GCD of $$3910$$ and $$3570 = 170$$

Area of the hall $$= 3910 \times 3570 = 13958700 cm^2$$

Area of one square tile $$= 170 \times 170 = 28900 cm^2$$

The number of tiles $$= \dfrac{13958700}{28900}$$

$$= 483 tiles$$
Question 5
1 / -0

How many metres of a carpet $$75$$ cm wide will be required to cover the floor of a room which is $$20$$ metres long and $$12$$ metres broad?

A
$$220$$ m

B
$$320$$ m

C
$$360$$ m

D
$$400$$ m

Solution

Given ,
For room , length $$=20\ m$$ and breadth $$=12\ m$$

Area of room $$=20\times 12=240\ m^2 -(1)$$

$$75\ cm=0.75\ m$$

Let $$l$$ be the length of carpet
Area of carpet required=$$l\times 0.75\ m^2~~~~~~~~-(2)$$

From eqs.(1) and (2)

$$\therefore l\times 0.75=240\\\to l=\dfrac{240}{0.75}=320\ m$$
Question 6
1 / -0

The perimeter of a rectangular garden is $$30$$ feet. If its length is $$6$$ feet, what is its width?

A
$$9$$ feet

B
$$10$$ feet

C
$$18 $$feet

D
$$21 $$feet

E
$$24 $$feet

Solution

The perimeter of a shape is the distance around it. In particular, the perimeter of a rectangle is given by the formula $$P = 2W + 2L$$. Substitute the correct values of the variables into this formula ($$P = 30$$ and $$L = 6$$) and then solve for the width W:
$$30= 2W + 2(6)$$
$$30= 2W+12$$
$$18= 2W$$
$$W=9$$
Therefore, the width of the garden is $$9$$ feet.
Question 7
1 / -0

Distance between two dots is $$1\,cm$$
Find the perimeter of Green Rectangle

A
$$12$$ cm

B
$$14$$ cm

C
$$15$$ cm

D
$$20$$ cm

Solution

$$\therefore$$ This is the given rectangle with distance between two dots $$=1cm$$
Length $$(l)=4cm$$
Breadth $$(b)=3cm$$
Perimeter of given rectangle $$=2(l+b)$$
$$=2(4+3)$$
$$=14cm$$
$$\therefore$$ Hence, option (B) is correct.
Question 8
1 / -0

The area of the floor of a rectangular shape of length $$20 m$$ is $$1200\:cm^2$$. Carpets of 4 cm $$\times$$ 6 cm are available. Find how many carpets are required to cover the hall.

A
$$40$$

B
$$50$$

C
$$60$$

D
None

Solution

The area of the rectangular floor is $$1200 { cm }^{ 2 }$$.
The dimension of the carpet is $$4 cm \times 6 cm$$.
Hence the area of the carpet is $$24$$ $${ cm }^{ 2 }$$.
Let the number of carpets be n.
For the carpets to completely cover the hall
$$\Rightarrow n \times 24 = 1200$$
$$\Rightarrow n = 50$$
Question 9
1 / -0

A rectangular grassy plot is $$112$$ m by $$78$$ m. If has a gravel path $$2.5$$ m wide all round on the inside. Find the area of the path and the cost of constructing it at Rs. $$2$$ per square metre?

A
$$923$$ sq. m, Rs. $$1846$$

B
$$925$$ sq. m, Rs. $$1850$$

C
$$940$$ sq. m, Rs. $$1880$$

D
none

Solution

Given,
Length of plot $$=112m,$$ Breadth $$=78m$$

Area of plot=$$112\times 78=8736m^2$$

Now After forming the path
The lenth of remaining plot $$l=112-2(2.5)=108m$$
Breadth $$b=78-2(2.5)=73m$$

Area of remaining plot $$=108\times 73=7811m^2$$

Area of path $$=8736-7811=925m^2$$

Cost of constructing
$$=Area\times rate\\=925\times 2\\=Rs1850$$
Question 10
1 / -0

A square and a rectangle have same perimeter. The side of square is $$40$$ cm and length of rectangle is $$10$$ cm, find breadth of rectangle.

A
$$80$$ cm

B
$$90$$ cm

C
$$70$$ cm

D
None

Solution

$$\displaystyle { P }_{ S }={ P }_{ R }$$

$${ P }_{ S }=40+40+40+40=160cm$$

$$\displaystyle { P }_{ R }=2\left( l \right) +\left( b \right) 2=2\left( l+b \right) =2\left( 10+b \right) cm$$

$$\therefore \displaystyle 160=2\left( 10+b \right) $$

$$\Rightarrow \displaystyle 80=10+b$$

$$\Rightarrow \displaystyle b=70$$cm

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Mensuration Test - 11

Result

Mensuration Test - 11

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SHARING IS CARING

Question 1

$$270\ m$$

$$230\ m$$

$$540\ m$$

None

Solution

Question 2

34900

35100

35900

36100

Solution

Question 3

$$64 sq. \ m$$

$$5.6 sq. \ m$$

$$4.8 sq. \ m$$

$$48 sq. \ cm$$

Solution

Question 4

$$480$$

$$483$$

$$467$$

$$487$$

Solution

Question 5

$$220$$ m

$$320$$ m

$$360$$ m

$$400$$ m

Solution

Question 6

$$9$$ feet

$$10$$ feet

$$18 $$feet

$$21 $$feet

$$24 $$feet

Solution

Question 7

$$12$$ cm

$$14$$ cm

$$15$$ cm

$$20$$ cm

Solution

Question 8

$$40$$

$$50$$

$$60$$

None

Solution

Question 9

$$923$$ sq. m, Rs. $$1846$$

$$925$$ sq. m, Rs. $$1850$$

$$940$$ sq. m, Rs. $$1880$$

none

Solution

Question 10

$$80$$ cm

$$90$$ cm

$$70$$ cm

None

Solution

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