Free Mensuration 03 Practice Test - 8th Grade

Question 1

The sides of a rectangle are in the ratio of 6 : 5 and its area is 750 sq.m. Find the perimeter of rectangle (in m).

120

110

122

None of these

SOLUTION

Solution : B

Let 6x and 5x be the sides of a rectangle.

$\Rightarrow 6 x \times 5 x = 750$

$\Rightarrow 30 x^{2} = 750$

$\Rightarrow x^{2} = \frac{750}{30} = 25$

$\Rightarrow x = 5$

Length = 6x = 30m

Breadth = 5x = 25m

Perimeter = 2(l + b) = 2(30 + 25) = 110m

Question 2

A mat in the shape of a parallelogram has a height of 4 cm and a base of 3 cm. How much would it cost to cover a parallelogram shaped hall with an area of 180 sq. cm with mats, if each mat costs Rs.7?

Rs. 105

Rs. 115

Rs. 135

Rs. 95

SOLUTION

Solution : A

Let n be the number of mats required

base of mat = 3 cm
height of mat = 4 cm

Area of the parallelogram = base $\times$ height

Area of hall = Area of mat $\times$ number of mats

$\Rightarrow$ 180 = 4 x 3 x n

$\Rightarrow n = \frac{180}{12} = 15$

Given that each mat costs Rs. 7

Then the cost of 15 mats costs = 7 x 15 = Rs.105

Question 3

The perimeter of the given figure is ___

SOLUTION

Solution :
A Perimeter is the boundary of any closed geometrical figure.

The perimeter of the given figure is the sum of arc length BC and the slant lengths AB and AC.

Arc is semicircle so its perimeter is $π r$

$P e r i m e t e r = π r + 2 \times S l a n t h e i g h t$
$= \frac{22}{7} \times 1.4 + 2 \times 2$

$\Rightarrow 4.4 + 4 = 8.4 c m$

Question 4

PQRS is a quadrilateral in which $P Q = 5 \sqrt{2} c m$ , $Q R = 5 \sqrt{2} c m$ , $R S = 8 c m$ , $S P = 6 c m$ , $∠ P S R = ∠ P Q R = 90^{\circ}$ . Then its area is

$40.4 c m^{2}$

$46.4 c m^{2}$

$32.4 c m^{2}$

$49 c m^{2}$

SOLUTION

Solution : D

Area of right angled triangle $Δ P Q R$
$= \frac{1}{2} \times B a s e \times H e i g h t = \frac{1}{2} \times 5 \sqrt{2} \times 5 \sqrt{2} = 25 c m^{2}$

Area of right angled triangle $Δ P S R$
$= \frac{1}{2} \times 8 \times 6 = 24 c m^{2}$

Area of quadrilateral PQRS
= Area of $Δ P Q R + Δ P S R = 49 c m^{2}$

Question 5

The capacity of a soda can be calculated using the formula.

2πr(r+h)

2πr

π $r^{2}$ h

All of these

SOLUTION

Solution : C

A soda can is a rough example of a cylinder.

The volume of a cylinder is $π r^{2} h$ .
The capacity of any vessel is its internal volume so, the capacity of a soda can be calculated using the formula $π r^{2} h$ .

Where,
r = base radius of the can

h = height of the can

Question 6

The volume of a cube whose edge is 24 m is 1296 m³ .

True

False

SOLUTION

Solution : B

Volume of cube = ${(e d g e)}^{3}$
Hence the volume of cube with edge 24 m is ${(24)}^{3}$
= 13824 $m^{3}$ .

Question 7

A cuboid whose length, breadth and height are equal is called a ___________.

Hexagon

Pentagon

Cube

Cuboid

SOLUTION

Solution : C

A cuboid whose length, breadth and height are equal is called a Cube. Cube is a special case of a cuboid in which all the sides are equal.

Question 8

If the height of a cylinder is halved and its diameter is doubled then, the new volume is the initial volume.

is equal to

is double of

is three times of

is four times of

SOLUTION

Solution : B

Let the radius of a cylinder be 'r' and the height of a cylinder be 'h'.
$Volume of cylinder = V = π r^{2} h New radius = 2 r New height = \frac{h}{2} New volume = π (2 r)^{2} \frac{h}{2} = 2 π r^{2} h New volume = 2 V$

Question 9

An isosceles trapezium has an area of 36 cm², the parallel sides are 12 cm and 6 cm respectively. The perimeter of the trapezium should be

28 cm

32 cm

24 cm

20 cm

SOLUTION

Solution : A

$The area of a trapezium is given by:$
$A = \frac{1}{2} \times (Sum of parallel sides) \times (height)$
$\Rightarrow 36 = \frac{1}{2} \times (12 + 6) \times h$
$\Rightarrow h = 4 c m$
$So now in the trapezium,$
$h = 4 c m$
$a = b = 6 c m$
$A B = C D [S-A-S congruency in △ A F B and △ D E C]$
$∴ 2 A B + a = 12 c m$
$\Rightarrow 2 A B = 12 - 6$
$\Rightarrow A B = C D = 3 c m$
$So now in △ A B F, A B^{2} + h^{2} = d^{2}$
$d^{2} = 3^{2} + 4^{2} = 25$
$d = 5 c m$
As the trapezium is isosceles, the slant sides of the trapezium are equal in length
$d = c = 5 c m$
$∴$ the perimeter of the trapezium
$= (2 \times A B) + a + c + b + d$
$= (2 \times 3) + 6 + 5 + 6 + 5 = 6 + 22 = 28 c m$

Question 10

Every quadrilateral has two pairs of parallel sides.

A. True

B. False

SOLUTION

Solution : B

A quadrilateral is a four- sided rectilinear figure and parallelogram is a four-sided plane rectilinear figure with opposite sides parallel. Square, rectangle are considered as parallelogram because both of them have opposite sides parallel. In trapezium, only one side is parallel hence, it is not considered as a parallelogram. Hence, every quadrilateral doesn't have two pairs of parallel sides.

Free Mensuration 03 Practice Test - 8th Grade

Question 1

SOLUTION

Question 2

SOLUTION

Question 3

SOLUTION

Question 4

SOLUTION

Question 5

SOLUTION

Question 6

SOLUTION

Question 7

SOLUTION

Question 8

SOLUTION

Question 9

SOLUTION

Question 10

SOLUTION

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Factorisation 02
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