Mensuration Class 8 MCQ Questions

Answer: (b) 77 cm²

Explanation: Given:

Length of one of the parallel side = 4 cm

Length of other parallel side = 7 cm

Distance between parallel sides = 14 cm

Area of trapezium = (1/2) x ( sum of two parallel sides ) x ( distance between them )

Area of trapezium = { (1/2) x ( 4 + 7 ) x 14 } cm²

Area of trapezium = { (1/2) x ( 11 ) x 14 }cm²

Area of trapezium = (154/2)cm²

Area of trapezium = 77 cm²

Answer: (b) 16 cm

Explanation: Given:

Area of trapezium = 120cm²

Distance between parallel sides = 10 cm

Length of one of the parallel side = 8 cm

Length of other parallel side = ?

Let the length of the other parallel side be y cm

Area of trapezium = (1/2) x ( sum of two parallel sides ) x ( distance between them )

120 cm² = {(1/2) x ( 8 + y ) x 10 } cm²

120 = 40 + 5y

120 – 40 = 5y

5y = 80

y = 80/5

y = 16

Hence, the length of other parallel side is 16 cm

Answer: (b) 9 cm and 11 cm

Explanation: Given:

Area of trapezium = 60 cm²

Distance between parallel sides = 6 cm

Difference between the length of parallel sides = 2 cm

Let the length of one parallel side be y cm

then, the length of other parallel side be ( y + 2 ) cm

Area of trapezium = (1/2) x ( sum of two parallel sides ) x ( distance between them )

60 cm² = { (1/2) x ( y + y + 2 ) x 6 } cm²

60 = { (1/2) x ( 2y + 2 ) x 6 }

60 = { ( 2y + 2 ) x 3

60/3 = 2y + 2

20 = 2y + 2

20 – 2 = 2y

18 = 2y

y = 18/2

y = 9

Therefore,

Length of one of its parallel side = y cm = 9 cm

Length of other parallel side = ( y + 2 ) cm = ( 9 + 2 ) cm = 11 cm

Answer: (c) 4 cm

Explanation: Given:

Area of trapezium = 64 cm²

Distance between parallel sides = 8 cm

Ratio of its parallel sides = 1 : 3

Let the length of one parallel side be 1y cm

then, the length of other parallel side would be 3y cm

Area of trapezium = (1/2) x ( sum of two parallel sides ) x ( distance between them )

64 cm² = { (1/2) x ( 1y + 3y ) x 8 } cm²

64 = { (1/2) x ( 4y ) x 8 }

64 = ( 4y x 4 )

64/(4×4) = y

y = 4

Therefore,

Length of one of its parallel side = 1y cm = ( 1 x 4 ) cm = 4 cm

Length of its other parallel side = 3y cm = ( 3 x 4 ) cm = 12 cm

Hence, the length of the smaller side is 4 cm

Answer: (a) 90 cm²

Explanation: Given:

Base = 12 cm

Height = 15 cm

As we know that,

Area of triangle = (1/2) x Base x Height

Area of triangle = ( (1/2) x 12 x 15 ) cm²

Area of triangle = 90 cm²

Answer: (c) 8 cm

Explanation: Given:

Area of triangle = 24 cm²

Base = 6 cm

Height = ?

Let,

the height of the triangle be = y cm

As we know that,

Area of triangle = (1/2) x Base x Height

24 = (1/2) x 6 x y

(24×2)/6 = y

y = 8

Hence, the length of the height of the Triangle would be 8 cm

Answer: (c) 24 cm

Explanation: Given:

Area of triangle = 180 cm²

Height = 15 cm

Base = ?

Let,

the Base of the Triangle = y cm

As we know that,

Area of triangle = (1/2) x Height x Base

180 = (1/2) x 15 x y

(180×2)/15 = y

y = 24

Hence, the length of the base of the Triangle would be 24 cm

Answer: (b) 133 cm²

Explanation :​

BE ⏊ AC

DF ⏊ AC

AC = 14 cm

BE = 12 cm

DF = 7 cm

Area of quad. ABCD = Area of ∆ABC + Area of ∆ADC

Area of ∆ABC = { (1/2) x base x height }

Area of ∆ABC = { (1/2) x AC x BE }

Area of ∆ABC = { (1/2) x 14 x 12 } cm²

Area of ∆ABC = 84 cm²

Area of ∆ADC = { (1/2) x base x height }

Area of ∆ADC = { (1/2) x AC x DF }

Area of ∆ADC = { (1/2) x 14 x 7 } cm²

Area of ∆ADC = 49 cm²

Area of quad. ABCD = Area of ∆ABC + Area of ∆ADC

Area of quad. ABCD = 84 cm² + 49 cm²

Area of quad. ABCD = 133 cm²

Answer: (b) 13454 Litres

Explanation: We are given that

Length of water tank ( l ) = 1m 40cm

= (1+(40/100)m   (1cm=(1/100)m)

= ( 1 + 0.4 )m

= 1.4m

Breadth of water tank ( b ) = 3m 10cm

= (3+(10/100))m    (1cm=(1/100)m)

= 3 + 0.1

= 3.1m

Height of water tank ( h ) = 3m 10cm

= (3+(10/100))m    (1cm=(1/100)m)

= ( 3 + 0.1 )m

= 3.1m

Capacity of water tank = Volume of water tank

Volume of water tank = l x b x h

= ( 1.4 x 3.1 x 3.1 ) m³

Now 1 m³ = 1000 Litres

So, 13.454 m³ = 13.454 x 1000 Litres of water

= 13454 Litres of water

Answer: (a) ₹ 2240

Explanation: In this question we are given

Area of courtyard = 3200 m²

Height of gravel required = 7cm

= (7/100)m (1cm=(1/100)m)

= 0.07m

Volume of gravel = Area of courtyard x Height of gravel

= 3200 x 0.07

= 224m³

Costs of 1m³ gravel = ₹ 10

Costs of 224m³ gravel = ₹ 10 x 224

= ₹ 2240

Answer: (c) 16.73m

Explanation: Dimensions of room are given as

Length (l) = 6m

Breadth (b) = 12m

Height (h) = 10m

Longest pole that can be put in a room, Diagonal (d) =√l²+b²+h²

= √6²+12²+10²

= √36+144+100

= √280

= 16.73m ( approx )

Answer: (b) 45000

Explanation: Length of wall = 12m

= 12 x 100 = 1200cm

Breath of wall of wall = 10cm

Height of wall = 15m

= 15 x 100 = 1500cm

Volume of wall = L x B x H

= ( 1200 x 10 x 1500 ) cm³

Volume of 1 brick = l x b x h

Dimensions of brick

l = 8cm

b = 10cm

h = 5cm

Volume = ( 8 x 10 x 5 ) cm³

Number of brick required = Volume of wall

Volume of 1 brick

= (1200×10×1500)/8×10×5

= 45000

So, the Number of brick required to build the wall = 45000

Answer: (b) 450 persons

Explanation: To find the number of persons that can be accommodated in a hall

We have to find the Volume of hall

Dimensions of hall are given as under

Length of hall ( l ) = 12m

Breadth of hall ( b ) = 15m

Height of hall ( h ) = 10m

Volume of hall = l x b x h

= ( 12 x 15 x 10 ) m³

= 1800m³

Volume of air required by each persons = 4m³

Number of persons that can be accommodated in a hall = Volume of hall / Volume required by each person

= 1800/4

= 450

So, the Number of persons that can be accommodated in a hall = 450 persons

Answer: (b) Lateral surface area of a Cuboid = 270m² , Total surface area of a Cuboid = 702m²

Explanation: We are given that,

Length of Cuboid ( l ) = 18m

Breadth of Cuboid ( b ) = 12m

Height of Cuboid ( h ) = 4.5m

Lateral surface area of a Cuboid = 2 ( l + b ) x h

= 2 ( 18 + 12 ) x 4.5

= 2 x 30 x 4.5

Lateral surface area of a Cuboid = 270 m²

Total surface area of a Cuboid = 2 ( l b + b h + h l )

= 2 ( 18 x 12 + 12 x 4.5 + 4.5 x 18 )

= 2 ( 216 + 54 + 81 )

= 2 x 351

Total surface area of a Cuboid = 702 m²

Answer: (c) 100 hours

Explanation: Volume of reservoir = 300m³

= 300 x 1000 ( 1 m³ = 1000 litres )

= 300000 litres

Rate of flow of water = 50 litres per minute

Time taken to fill the reservoir =Volume of reservoir in litres/Rate of flow of water in litres per minute

=(300000/50)min

= 6000 min

=(6000/60)hours ( 1 min = 1/60 hours )

= 100 hours

Answer: (b) 220 m³

Explanation: We are given that,

Length of Cuboid ( l ) = 8m

Breadth of Cuboid ( b ) = 5m

Height of Cuboid ( h ) = 5.5m

Volume of Cuboid is l x b x h

Therefore,

Volume of Cuboid = ( 8 x 5 x 5.5 ) m³

= 220 m³

Answer: (b) 3402 cm³

Explanation: External length = 12cm

External breadth = 20cm

External height = 15cm

Thickness = 4.5cm

Therefore,

Internal length = ( External length – 2 x Thickness )

= ( 12 – 2 x 4.5 )

= ( 12 – 9 ) cm

= 3cm

Internal breadth = ( External breadth – 2 x Thickness )

= ( 20 – 2 x 4.5 )

= ( 20 – 9 ) cm

= 11cm

Internal height = ( External height – 2 x Thickness )

= ( 15 – 2 x 4.5 )

= ( 15 – 9 ) cm

= 6cm

Now,

Volume of the wood required to make the box = External volume – Internal volume

= ( External length x External breadth x External height ) – ( Internal length x Internal breadth x Internal height )

= ( 12 x 20 x 15 ) – ( 3 x 11 x 6 )

= 3600 – 198

= 3402cm³

Answer: (a) 4m

Explanation: Length of the swimming pool = 200m

Breadth of the swimming pool = 180m

Volume of water pumped into it = 144000 m³

Volume of water = length x breadth x height

144000 = 200 x 180 x h

h x 200 x 180 = 144000

h =144000/(200×180)

= 144000/36000

= 4m

Hence, the height of water level in swimming pool is = 4m

Answer: (c) Curved surface area of cylinder = 7700 cm ² , Total surface area of cylinder = 1408 cm ²

Explanation: We are given that,

Height of cylinder ( h ) = 25cm

Radius of cylinder ( r ) = 7cm

Curved surface area of cylinder = (2πrh)sq units

=(2×(22/7)×7×7×25)cm²

Curved surface area of cylinder = 7700 cm²

Total surface area of cylinder = 2πr(h+r)sq units

= 2×(22/7)×7(7+25)

= 2×(22/7)×7×32

Total surface area of cylinder = 1408 cm²

Answer: (c) 14 m

Explanation: We are given that,

Capacity of cylindrical tank = 7436 m³

Diameter of its base = 26m

Radius = 12 x Diameter

= 12 x 26 m

= 13m

Let the Depth (height) of cylindrical tank be h m

Capacity of cylindrical tank = Volume of cylindrical tank

Since,

Volume of cylindrical tank =πr²h cubic units​

7436 = ( (22/7) x 13 x 13 x h )

(22/7) x 13 x 13 x h = 7436

On cross multiplication,

h = (7436×7)/22×13×13

h = 52052/3718

h = 14m

Hence, Depth of cylindrical tank = 14m

Answer: (b) 3 : 2

Explanation: We are given that,

Radius of cylinder = 10cm

Height of cylinder = 15cm

As we know the formulas

Curved surface area of cylinder = 2πrh sq units

Total surface area of cylinder = 2πr(h+r)sq units

We have to find the ratio of Curved surface area and Total surface area

So,

Curved surface area of cylinder : Total surface area of cylinder

2πrh : 2πr(h+r)

2πr From both the sides will be cancelled out

h : ( h + r )

15 : 10

3 : 2

Hence, The ratio of Curved surface area and Total surface area = 3 : 2

Answer: (a) 554.4 m³

Explanation: We are given that,

Height of cylinder = 4.9m

Radius of cylinder = 6m

Volume of cylinder is πr²h cubic units

Therefore,

Volume of cylinder = ((22/7)×6×6×4.9)m³

= 554.4 m³

Hence, the Volume of cylinder = 554.4 m³

Answer: (c) 20736 cm³

Explanation: We are given that,

Total surface area of cuboid = 456 cm²

Ratio of edges of cuboid = 1 : 3 : 4

Let the sides of cuboid be 1x , 3x and 4x

Total surface area of cuboid = 2( lb + bh + hL )

456 = 2x( 1x x 3x + 3x x 4x + 4x x 1x )

456 = 2 x ( 3x + 12x + 4x )

456 = 2 x 19x

38x = 456

x = 456/38

= 12

Edges of cuboid = 1x

= 1 x 12 = 12cm

= 3x

= 3 x 12 = 36cm

= 4x

= 4 x 12 = 48cm

Volume of cuboid = l x b x h

= 12 x 36 x 48

= 20736 cm³

Answer: (b) 6160 cm³

Explanation: Since, the rectangular shape of paper is rolled along its width

Therefore, the height of the cylinder so formed would be 10cm

So,

Height of cylinder = 10cm

Radius of cylinder = 14cm

We know that,

Volume of cylinder = πr²h cubic units

=((22/7)×14×14×10)cm³

= 6160 cm³

Hence, the Volume of cylinder is = 6160 cm³

Answer: (b) 21296 m³

Explanation: Curved surface area of a cylinder = 121 m2

Height of a cylinder (h) = 14m

We know that,

Curved surface area of a cylinder = (2πrh) sq units

121 = (2πrh) sq units

121 = 2 x (22/7) x r x 14

2 x (22/7) x r x 14 = 121

r = (121×7)/2×22×14

r = (5.5×7)/2×14

= (5.5×1)/2×2

r = 5.5/4

Volume of a cylinder = πr²h cubic units

= ((22/7)×(5.5/4)×(5.5/4)×14 ) m³

Volume of cylinder = 21296 m³

Answer: (a) 18 kg

Explanation : We are given that,

Length of iron beam = 10m

Width of iron beam = 20cm

= 20/100 m ( 1cm = 1/100 m )

Height of iron beam = 30cm

= 30/100 m ( 1cm = 1/100 m )

Volume of iron beam = Length x Width x Height

= 10 x (20/100) x (30/100) m³

if 1 cubic metre of iron weighs = 30 kg

Weight of iron beam = 10 x (20/100) x (30/100) x 30 kg

= 180000/10000

= 18 kg

Answer: (c) 700 kg

Explanation: Length of rectangular piece of iron ( l ) = 14m

= 14 x 100 cm ( 1m = 100cm )

= 1400cm

Breadth of rectangular piece of iron ( b ) = 10cm

Height of rectangular piece of iron ( h ) = 5cm

Volume of rectangular piece of iron = l x b x h

= ( 1400 x 10 x 5 ) cm³

We need to find the weight of of rectangular piece of iron = 70000 cm³

Weight of 1 cm³ of iron = 10 grams

Weight of 70000cm³ of iron = 10 x 70000

= 700000

= 700000 grams

= 700000/1000 Kg (1gm=1/1000Kg)

= 700 Kg

Answer: (b) 50 cm

Explanation: Area of the field = length of the field x breadth of the field

Area of the field = 30 x 70

= 2100 m²

Are of the pit = length of pit x breadth of pit

= 20 x 5

= 100 m²

Area over which the earth is spread out = ( Area of the field – Are of the pit )

= ( 2100 – 100 ) m²

= 2000 m²

Volume of earth dug out will be equal to the volume of = length of pit x breadth of pit x depth of pit

= 20 x 5 x 10

= 1000 m³

Rise in the level of the field = Volume of earth dug out

Area over which the earth is spread out

= 1000/2000

= 0.5m

= 0.5 x 100 cm ( 1m = 100cm )

= 50cm

Hence, the rise in the level of the field = 50cm

Answer: (a) 61600 m³

Explanation: We are given that,

Circumference of circular base of cylinder = 440cm

Height of cylinder = 4cm

Circumference of circle = 2πr

440 = 2πr

2 x (22/7) x r = 440

r = (440/44) x 7

r = 70cm

Volume of cylinder = πr²h cubic units

= ( (22/7) x 70 x 70 x 4 ) cm³

Volume of cylinder = 61600cm³

Answer: (c) 10 : 9

Explanation: We are given that,

Ratio of radii of two cylinders = 4 : 3

Ratio of heights of two cylinders = 5 : 8

Let the radii of two cylinders be 4r and 3r

And heights of two cylinders be 5h and 8h

Volume of cylinder = πr²h cubic units

Therefore, the ratio of Volume of two cylinders

π x 4r x 4r x 5h : π x 3r x 3r x 8h

π will be cancelled out from both the sides

4r x 4r x 5h : 3r x 3r x 8h

80rh : 72rh

10 : 9

Hence, the ratio of Volume of two cylinders = 10 : 9

Answer: (a) 21.78 kg

Explanation: We are given that,

External radius of iron pipe = 7cm

Thickness of the pipe = 3cm

Length of the pipe = 21cm

Internal radius = ( External radius – Thickness of the pipe )

= ( 7 – 3 ) cm

= 4cm

External volume of the pipe = πR²H cubic units

= ( (22/7) x 7 x 7 x 21 ) cm³

= 3234 cm3

Internal volume of the pipe = πr2hcubicunits

= ( (22/7) x 4 x 4 x 21 ) cm³

= 1056 cm³

Volume of iron = External volume of the pipe – Internal volume of the pipe

= ( 3234 – 1056 ) cm³

= 2178 cm³

Weight of iron = 10 g/cm³

Weight of the pipe = 10 x 2178 g

= 21780 g

Or,

Weight of the pipe = 21780/1000 kg ( 1 g = 1/1000 kg )

= 21.78 kg