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Region enclosed by a plane figure - class-VI

Description: region enclosed by a plane figure
Number of Questions: 22
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Tags: mensuration-i (area) maths perimeter and area of rectilinear figures area
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The standard unit of volume is in

  1. $m$

  2. $m^2$

  3. $m^3$

  4. None of the above


Correct Option: C
Explanation:

For eg., a cube is a $3D$ object.

$\therefore$ volume of a cuboid $=$ $l \times b \times h$
All the three dimensions are measures in "meter".
Hence, the unit of measure measurement of volume is in cubic meter or $m^3$.
So, option C is correct.

Area is measured in____

  1. sq units

  2. cm units

  3. cu units

  4. none of these


Correct Option: A
Explanation:

area is measured in sq units..(cm x cm or mt x mt)

The amount of surface enclosed by a closed plane figure is called its ...............

  1. Area

  2. Perimeter

  3. Volume

  4. None of these


Correct Option: A
Explanation:

The amount of surface enclosed by a closed plane figure is called its 

AREA

$1000$ ml is equal to

  1. $1:cm^3$

  2. $10:cm^3$

  3. $100:cm^3$

  4. $1000:cm^3$


Correct Option: D
Explanation:

We know that,  $ 1  m^3 = 1000 l$

Also $100 cm = 1 m$ and $1 l = 1000ml$
Hence $1000 ml  = 1 l =  \dfrac{1}{1000} m^3 = \dfrac{1}{1000}\times (100 cm )^3=1000 cm^3$

$1:cm^3$ is equal to

  1. $1$ ml

  2. $10$ litres

  3. $1000$ ml

  4. $100$ litres


Correct Option: A
Explanation:

We know that, $ 1  m^3 = 1000$ $l$

Also, $100$ cm $= 1$ m and $1 $ $ l$ $= 1000$ ml
Hence, $1 m^3 = (100)^3cm^3 = 1000(1000)$ ml
$\Rightarrow 1 cm^3 = 1 $ ml

............. is expressed in square units.

  1. Perimeter

  2. Area

  3. Square

  4. Rectangle


Correct Option: B
Explanation:

Area can be expressed in square units.

Area is ____

  1. $1$ - dimensional

  2. $2$ - dimensional

  3. $3$ - dimensional

  4. $4$ - dimensional


Correct Option: B
Explanation:

Area is $2$ - dimensional.
Because it has length and width.

Amount of region of space occupied by a solid is called

  1. Area

  2. Volume

  3. Surface area

  4. None


Correct Option: B
Explanation:

Volume means the magnitude of 3D space enclosed within or occupied by an object.

What is quantity that a container can hold is called?

  1. Surface area

  2. Lateral surface area

  3. Volume

  4. None


Correct Option: C
Explanation:

Volume is the amount of space that a substance or object occupies or that is enclosed with in container.

The amount of surface enclosed by a closed figure is called its

  1. volume

  2. area

  3. space

  4. perimeter


Correct Option: B
Explanation:

Amount of surface enclosed by a closed figure is called its area.

The cubic unit is used to measure

  1. speed

  2. area

  3. volume

  4. perimeter


Correct Option: C
Explanation:

The cubic unit is used to measure volume.

State true or false.

The volume of the solid is measured in cubic units.

  1. True

  2. False


Correct Option: A
Explanation:

All volumes are measured in cubic units, as it is the space occupied in all the three dimensions. So, when we talk about volume, actually we talk about length, width and height of the solid.

Area is the total surface covered by a closed figure is 

  1. True

  2. False

  3. Anomalous

  4. None of these


Correct Option: A
Explanation:

Yes the region covered by the enclosed figure or the total surface covered is the area of the particular shape.True.Option A

Area is measured in

  1. units

  2. cubic units

  3. square units

  4. cm


Correct Option: C
Explanation:

The measurement of area is done in square units.

Area is the length of the boundary of a closed figure.

  1. True

  2. False

  3. Either

  4. Neither


Correct Option: B
Explanation:

Length of the boundary is the Perimeter not the area. The region enclosed inside the boundary is the area.
Therefore the statement is false.
Option B

Volume is measured in _____ units.

  1. square

  2. cubic

  3. unit

  4. cubic meter


Correct Option: B
Explanation:

Volume is measured in cubic units.

Two pipes can fill a tank in $20$ and $24$ minutes respectively and a waste pipe can empty $3$ gallons per minute. All the three pipes working together can fill the tank in $15$ minutes. The capacity of the tank is :

  1. $60\ gallons$

  2. $100\ gallons$

  3. $120\ gallons$

  4. $180\ gallons$


Correct Option: C
Explanation:

According to given question,

 Two ppes can fill atank $=20\,and\ 24\,\min .$

A waste pipe can empty$=3\,gallon/\min .$

Three pipes working$=15\,\min .$


So, According to given question,

Work done by the waste pipe in 1 minute

$ =\dfrac{1}{15}-\left( \dfrac{1}{20}+\dfrac{1}{24} \right) $

$ =\dfrac{1}{15}-\dfrac{11}{120} $

$ =-\dfrac{1}{40} $


Note:- negative sign means emptying

Then,

Volume of $\dfrac{1}{40}\,part$ $=\,3\,gallons.$

Volume of whole$=3\times 40=120\,gallons.$


Hence, this is the answer.

______ is expressed in square units.

  1. Perimeter

  2. Area

  3. Square

  4. Rectangle


Correct Option: B
Explanation:

The area of a flat, or plane figure is the number of unit squares that can be contained within it.

So, area is expressed in square units.
Hence, the answer is area.

The amount of surface enclosed by a closed plane figure is called its _____

  1. area

  2. perimeter

  3. volume

  4. none


Correct Option: A
Explanation:

The amount of surface enclosed by a closed plane figure is called its area.

Hence, the answer is area.

The length and breadth of a room are in the ratio of 3 : 2. Its height is equal to half of its length. If the cost of carpeting the floor at Rs. 4.00 per m$^2$ is Rs. 216, then the area offour walls (in m$^2$) is

  1. 135

  2. 140

  3. 125

  4. 120


Correct Option: A
Explanation:

Let the length and breadth be 2x and 3x respectively. Then, floor area $= 6x^2$ sq.m. 
Cost of flooring at the rate of Rs. 4.00 per $m^2 = $ Rs. 216
$\therefore 6x^2 \times 4 = 216$
or $x^2 = 9$
or $x = 3$
$\therefore $ Length = 3x = 9m
Breadth = 2x = 6m
and Height $= \displaystyle \frac{1}{2} \times$ Length = 4.5 m
$\therefore $ Area of four walls = 2(length $\times$ height + breadth $\times$ height)
$=2 [9 \times 4.5 + 6 \times 4.5] = 135 m^2$

One side of a square is $4$ ft long. What is its area?

  1. 6 $ft^2$

  2. 4$ft^2$

  3. 8 $ft^2$

  4. 16 $ft^2$


Correct Option: D
Explanation:

Area of a square = $side \times  side$
one side = 4 ft
Area = $4^2$
Area = $16$ $ft^2$

The perimeter of a rhombus is 100 cm and one of the diagonals is 40 cm, Then the area of the rhombus is

  1. 1000 cm$^2$

  2. 500 cm$^2$

  3. 1200 cm$^2$

  4. 600 cm$^2$


Correct Option: D
Explanation:

Given that, perimeter of rhombus is $100cm$ and one diagonal $40cm$

Perimeter of rhombus=4$\times $side

So side$=25cm$

And we know that in a rhombus diagonal divides rhombus in two eauilateral triangle.

Area of one triangle:- s$=(25+25+40)/2 =45$

So area=(s$\times $(s-a)$\times $ (s-b)$\times $(s-c))^1/2

= (45$\times $(45-40)$\times $(45-25)$\times $(45-25))^1/2

$= 300cm^2$

So total area is 300$\times $2=600cm^2

 

Hence, this is the answer.

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