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This mock test of Olympiad Test: Mensuration for Class 8 helps you for every Class 8 entrance exam.
This contains 20 Multiple Choice Questions for Class 8 Olympiad Test: Mensuration (mcq) to study with solutions a complete question bank.
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students definitely take this Olympiad Test: Mensuration exercise for a better result in the exam. You can find other Olympiad Test: Mensuration extra questions,
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QUESTION: 1

The parallel sides of a trapezium are 25 cm and 13 cm. Its non-parallel sides are equal, each being 10 cm. Find the area of the trapezium.

Solution:

Area of trapezium= 1/2*d*(a+b) sq. Units.

Where d= perpendicular distance between parellel sides which are a & b respectively, 25 &13 cm.

25–13=12, 12/2= 6 cm is base of RT. Angled ∆.

Non parallel sides=10cm, this is hypotenuese of this ∆.

Find ‘d ‘ to solve.

d=√{10^{2}–6^{2}}=8 cm.

Area of trapezium= 1/2*8*(25+13)=152 cm^{2}

QUESTION: 2

Find the area of the given quadrilateral.

Solution:

Quad ABCD is made of two triangles ADC and ABC

so, area(ABCD) = area(ABC) + area(ADC)

= 4 x 12/2 + 3.5 x12/2

= 24 + 21

= 45 cm^{2}

QUESTION: 3

Find the altitude of a trapezium, the sum of the lengths of whose bases is 6.5 cm and whose area is 26 cm^{2}.

Solution:

QUESTION: 4

Find the total surface area of a cube whose volume is 343 cm^{3}.

Solution:

volume=(side)^3

so, 343=(side)^3

cube root of 343=side

cube root of 343=7

side=7cm

Surface area=6(side)^2

Surface area=6 x 7^2

Surface area=6 x 49

Surface area=294 cm^2

QUESTION: 5

A cylindrical tank has a capacity of 5632 m^{3}. If the diameter of its base is 16 m, find its depth.

Solution:

QUESTION: 6

Find the area of a rhombus whose diagonals are of lengths 20 cm and 16 cm.

Solution:

Area of rhombus =1/2 ×d1×d2

Length of the one diagonal= 20 cm

Length of the other diagonal =16 cm

Area of the rhombus =1/2×20×16

= 1×10×16

= 160

The area of the rhombus is 160cm^2.

QUESTION: 7

Find the area of the given figure.

Solution:

QUESTION: 8

Surface area of a cuboid = __________

Solution:

Total Surface Area of Cuboid: 2(lb + bh + hl)

L = length

B = Breadth

H = Height

QUESTION: 9

Find the volume of a cuboid whose length is 8 cm, breadth 6 cm and height 3.5 cm.

Solution:

Length of the cuboid = 8 cm

Breadth of the cuboid = 6 cm

Height of the cuboid = 3.5 cm

Volume of the cuboid = length × breadth × height

= 8 x 6 x 3.5 = 168cm^{3}

Therefore,volume of the cuboid = 168cm^{3}

QUESTION: 10

A godown is in the form of a cuboid of measures 60 m × 40 m × 30 m. How many cuboidal boxes can be stored in it if the volume of one box is 0.8 m^{3}?

Solution:

QUESTION: 11

The perimeter of a trapezium is 52 cm. Its non-parallel sides are 10 cm each and the distance between two parallel sides is 8 cm. Find the area of the trapezium.

Solution:

Perimeter of a Trapezium=sum of all sides

52= sum of parallel sides +20

Sum of parallel sides = 32

Area of Trapezium=

1/2(Sum of parallel sides) x h

=1/2(32)*8 = 128cm^{2}

QUESTION: 12

The cost of papering the wall of a room, 12 m long, at the rate of Rs. 1.35 per square meter is Rs. 340.20. The cost of matting the floor at Re. 0.85 per square metre is Rs. 91.80. Find the height of the room.

Solution:

Let the length of room = l = 12 m

breadth of room = b m

height of room = h m

Cost of matting the floor @ Re. 0.85 per m^2 = Rs. 91.80

floor area = 91.80 / 0.85 = 108 m^2

⇒ l * b = 108

⇒ 12 * b = 108

⇒ b = 108/12

⇒ b = 9 m

cost of papering wall @ Rs. 1.35 per m^2 = Rs. 340.20

wall area is the lateral surface area.

wall area = lateral surface area = 340.20 / 1.35 = 252 m^2

⇒ 2h(l+b) = 252

⇒ 2h(12+9) = 252

⇒ 2h*21 = 252

⇒ h = 252/(2*21)

⇒ h = 6 m

Height of room is 6m.

QUESTION: 13

The area of a trapezium is 384 cm^{2}. Its parallel sides are in the ratio 3:5 and the distance between them is 12 cm. Find the length of each parallel side.

Solution:

QUESTION: 14

In the given figure find the area of the path.

Solution:

Area of Rectangle ABCD = 110*150 = 16500cm^{2}

Area of rectangle EFGH = (150-10)(110-10) = 14000cm^{2}

Area of path = 16500-14000 = 2500cm^{2}

QUESTION: 15

The area of a rhombus is 28 cm^{2} and one of its diagonals is 4 cm. Find its perimeter.

Solution:

QUESTION: 16

Find the side of a cube whose surface area is 2400 cm^{2}.

Solution:

QUESTION: 17

Find the height of a cuboid whose volume is 275 cm^{3} and base area is 25 cm^{2}

Solution:

Area of the base = Product of length and breadth

Volume of cuboid = Length x breadth x Height

= Area of its base x Height

275 = 25 x Height

Height = 275 / 25 cm

=11 cm

QUESTION: 18

Find the height of cuboid whose volume is 490 cm^{3} and base area is 35 cm^{2}.

Solution:

Volume of cuboid = base area × height

490 = 35 × height

height = 14cm.

QUESTION: 19

Surface area of a cube = _________

Solution:

QUESTION: 20

Solution:

Circumference of semi circle =

perimeter = sum of two sides + circumference = 4 + 5.5 = 9.5cm

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