Test: Mensuration- 1 - Class 8 MCQ

The given figure is made up of three simple shapes:

• One rectangle (BCEF) in the middle
• Two triangles, one on each side of the rectangle

Step 1: Area of the rectangle (BCEF)
Length = 20 cm
Breadth = 10 cm
Area of rectangle = 20 × 10 = 200 cm²

Step 2: Area of the two triangles (ΔABF and ΔDCE)
Both triangles are similar having same base and height, So their respective areas will also be same.
Base = 10 cm
Height = 6 cm
Area of one triangle = 1/2 ​× 10 × 6 = 30 cm²
Area of two triangles = 30 + 30 = 60 cm²

Step 3: Total area of the figure
Area = Area of Rectangle + Area of two triangles
Area = 200 + 60 = 260 cm²

Therefore, the area of the adjoining figure is 260 cm²

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

Cube Total Surface Area = 6a² = 6×7² = 6×49 = 294 cm²

Given
Curved Surface Area of cylinder = 294

CSA = 2πrh
2 × 22/7 × r × 10 = 294

44r/7 ×10 = 294
(440r)/7 = 294
440r = 2058
r = 4.68 ≈ 5 cm

So, option (b) is the correct answer.

To find the total surface area (TSA) of a cuboid, we use the formula:
TSA=2(lb+bh+hl)

Given:

• l = 15 cm
• b = 10 cm
• h = 20 cm

Total surface area = 2(lb + bh + hl)
= 2(15 × 10 + 10 × 20 + 20 × 15)
= 2(150 + 200 + 300) = 2 × 650 = 1300 cm²
Correct answer: 1300 cm²

The correct answer is Option B - 7 m

Area of the square = 14² = 196 m².

Area of the circle = πr².

Equating the areas gives πr² = 196.

So r = √(196/π) = 14/√π.

Using π ≈ 3.1416, we get r ≈ 7.90 m.= 8 m

Among the given choices, the nearest value is 8 m, so the correct option is Option B.

In Cuboid,
Base Area = Length × Breadth
Volume = Length × Breadth × height
So, we can write as:
Volume of a cuboid = Base area × Height
Height = Volume / Base area
H = 275/25 = 11 cm

The correct answer is Option C - 209 m

Let the width be w and the length be 2w.

The area is given by length × width = 2w × w = 2w², and this equals 2420; so 2w² = 2420.

Thus w² = 1210, so w = √1210 (take the positive root for a length).

The perimeter is 2(l + w) = 2(2w + w) = 6w, so P = 6√1210.

Numerically, √1210 ≈ 34.785, hence P ≈ 6 × 34.785 = 208.71 m ≈ 209 m

Volume = 6×5×4 = 120 m³
1 m³ = 1000 L
So capacity = 120000 L

The correct answer is Option A - 40 cm²

Area = ½ × d₁ × d₂

Substituting d₁ = 10 cm and d₂ = 8 cm.

Area = ½ × 10 × 8 = ½ × 80 = 40 cm²

The total surface area of a right circular cylinder is calculated using the formula:

Total Surface Area = 2πr (r + h)

Given:

• r = 5 cm
• h = 10 cm

Substituting these values into the formula gives:

Total Surface Area = 2π × 5 × (5 + 10)

Total Surface Area = 10π × 15

Total Surface Area = 150π cm²

The correct answer is Option C - 294 cm²

Use the formula 6a² for the total surface area of a cube, where a is the side length.

Here a = 7 cm.

So a² = 49 cm².

Now compute 6 × 49 = 294.

Therefore the total surface area is 294 cm², which corresponds to Option C.

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 

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.

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.

The total surface area (TSA) of a cylinder includes the areas of the two circular bases and the lateral surface area. The formula is derived as follows:

• Area of the two circular bases: 2 × πr²
• Lateral surface area: 2πrh
• Total Surface Area: 2πr² + 2πrh = 2πr(r + h)

Thus, the correct answer is option B.

Base =  7 cm
Height  = 4 cm
Area of  Rhombus = Base × Height
= 7 × 4
= 28 cm²