Test: Mensuration- 1 - Class 8 MCQ

Area of square having sides 5 cm = 5² = 25 cm²

Area of smaller square having sides 1 cm = 1² = 1 cm²

Then area of 4 squares will be 4 cm²

Area of shaded portion will be =  Area of square having sides 5 cm - area of 4  smaller squares (Unshaded portion)

 Area of shaded portion = 25 cm² - 4 cm²

 Area of shaded portion = 21 cm²

Base and height of ΔABF and ΔCED are same. Thus their respective areas will be same.

Total area = (Area of △ABF)×2+Area of rectangle BCEF

Total area = (1/2×10×6)×2+(10×20) = 60+200

Total area = 260cm²

Area of Trapezium Derivation Using a Parallelogram: 
To derive the formula for the area of a trapezium using parallelogram, we will consider two identical trapeziums, each with bases a and b and height h. Let A be the area of each trapezium. Assume that the second trapezium is turned upside down as shown in the figure below.

We can see that the new figure obtained by joining the two trapeziums is a parallelogram whose base is a + b and whose height is h. We know that

• the area of a parallelogram is base × height = (a + b) h.
• the area of the above parallelogram in terms of 'A' is, A + A = 2A.

Thus, 2A = (a + b) h

⇒ A = (a+b)h/2

Thus, the formula for the area of a trapezium is derived. where a and b are parallel sides and h is height.

Area of Rectangle = product of length and breadth (L * B)
Area of Parallelogram = A = ½ × d₁ × d₂ sin (y) where d1 & d2 are diagonal and y is the angle of intersection of diagonal.
 
Area of Trapezium = 1/2(sum of parallel sides)*height. 

Area of Rectangle = Length * Breadth.
Area of Rhombus Using DiagonalsA = ½ × d₁ × d₂
Area of quadrilateral willl be calculated based on which type of quadriateral it is-
Area of trapezium willl be 1/2 (sum of Parallel sides )*height.

Given that, the length of one side of the trapezium b1 = 6cm and another is b2 =14cm.
The height of the trapezium h = 5cm.
Drawing the figure from the given data.

Area of Trapezium  = 1/2 (sum of Parallel sides ) * height
let a and b are the parallel sides:
a= 4cm
b= 6 cm
h= 3cm
according to formula -> 1/2(4+6)*(3)
=>1/2(10)(3)
=>30/2
=>15 cm²

2D definition - A two-dimensional (2D) object is an object that only has two dimensions, such as a length and a width, and no thickness or height. 
3D definition- A three-dimensional (3D) object is an object with three dimensions: a length, a width, and a height. The flat sides of three-dimensional objects are two-dimensional shapes.
Cuboid has length and width as well as thickness or height.

A cone is a three-dimensional figure which has a circular base and a curved surface.

A Sphere is three dimensional figure because it has volume.

Circle is the 2D figure because it does not have thickness

So the correct option will be D

Chalk box and soap have breadth,length and height . Cylinder has 2 radii and height. A ring (here) is made up of two concentric circles which is a 2d figure. Hence ring is 2 dimensional

2D definition - A two-dimensional (2D) object is an object that only has two dimensions, such as a length and a width, and no thickness or height.  Since the plane figure has no thickness or height so it will be 2d figure.

3D definition- A three-dimensional (3D) object is an object with three dimensions: a length, a width, and a height
Since solid figure has length breadth as well as thickness or height so sthe solid figure will be 3d. hence option B is correct.

3D figures appear in space. Since square,triangle and rectangle appear on plain, that is, paper, sphere is the only 3D object.

Since pyramid has length ,width and height so it will be 3D

From the above figure we can see that the line segments joining the centre of circular faces is perpendicular to the base.

Definition of Area : The space enclosed by the boundary of a plane figure.
Surface area: It is same as area in simple we can say that the amount of space enclosed by the surface.
Voume : It is defined as the amount of Space occupied by any three dimensional object.
Lateral surface area: it is defined as the space enclosed by any lateral surfaces.
So the option C is correct

Volume is nothing but multiplication of Length breadth and height:
V = L * B * H
SI unit of Length is m (Meter)
so as the breadth and height.
SI unit of Volume =  m * m * m
=> m³ .
Hence option c is correct.

Total surface area of cube = 6a²

Curved surface area of cube = 4a² 

Volume of cube = a³

Surface area of cube = 6 * Side of cube²  
Let a = side of cube.
a = 2m.
Surface area of cube = 6 * 2 * 2
     => 24 m² .
Hence option C is correct.

Lets break the figure -
It has 6 surfaces.
Area of bottom surface = L * B
Area of Top Surface = L * B
Area of Right side surface = B * H
Area of Left Side surface  = B * H
Area of front Surface = H * L
Area of Back surface = H * L 
Total surface area of Cuboid = sum of all the surfaces.
=> (Bottom surface area + Top surface area + Right side surface area + Left side surface area + front side surface area
back side surface area)
=> (LB + LB + BH + BH + HL + HL)
=> (2LB + 2BH + 2HL)
=> 2(LB + BH + HL)
hence option B is correct.

Lateral surface area -> Total Surface area of cuboid - surface area of Top and Bottom Surfaces.
=> 2LB + 2BH + 2HL - LB - LB
=> 2BH + 2HL
=> 2H(L + B)
hence option A is correct 

Since we have area of wall as b*h and h*l .So area of 4 walls is 2h*b+2h*l=2h(b+l)

Since all side is cube is same 
so the volume of cube is = side of cube * side of Cube * side of cube
lets take side of cube = l 
=> l*l*l
=> l³ 
Hence the correct option is A

The quantity that a container holds is called its "capacity" or "volume."

Hence option C is correct.

The conversion from cubic meters (m³) to liters (L) is based on the fact that 1 liter is equal to 1 cubic decimeter (dm³). Since 1 meter is equal to 10 decimeters, the conversion factor from cubic meters to liters is 10³

Therefore, to convert cubic meters to liters, you multiply the volume in cubic meters by 10³.

For a 1 cubic meter container:

1 m³×10³ L/m³=1000 L

So, 1 cubic meter is indeed equal to 1000 liters.

Base area = length * breadth = 20 sq.cm
Now,
Volume of cuboid = length * breadth * height
Volume = 20 * height
200 = 20 * height
Height = 200 / 20 = 10 cm.

1m³ = 1000 L and 1m³=1000000cm³ and 1000L= 1000000ml
So 1000000cm³ = 1000000ml which is 1ml = 1cm³

Lets  take the original side of cube be S, and final side be 2S.
Orginal surface area will be => 6 * S * S
Final surface area will be => 6 * 2S * 2S
=> 4 * (6 * S * S)
=> 4 times orginal surface area.
Hence the option C is correct.

Total surface area of a cylinder = πr²+2πrh+πr²=2πr(r+h)