# Free Mensuration 03 Practice Test - 8th Grade

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).

A.

120

B.

110

C.

122

D.

None of these

#### SOLUTION

Solution : B

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

6x×5x=750

30x2=750

x2=75030=25

x=5

Length = 6x = 30m

Breadth = 5x = 25m

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

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?

A.

Rs. 105

B.

Rs. 115

C.

Rs. 135

D.

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 × height

Area of hall = Area of mat × number of mats

180 = 4 x 3 x n

n=18012=15

Given that each mat costs Rs. 7

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

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 πr

Perimeter=πr+2×Slant height
=227×1.4+2×2

4.4+4=8.4cm

PQRS is a quadrilateral in which PQ=52cm, QR=52cm, RS=8cm, SP=6cm, PSR=PQR=90. Then its area is

A.

40.4 cm2

B.

46.4 cm2

C.

32.4 cm2

D.

49 cm2

#### SOLUTION

Solution : D Area of right angled triangle ΔPQR
=12×Base×Height=12×52×52=25 cm2

Area of right angled triangle ΔPSR
=12×8×6=24 cm2

Area of quadrilateral PQRS
= Area of ΔPQR+ΔPSR=49 cm2 The capacity of a soda can be calculated using the formula.

A.

2πr(r+h)

B.

2πr

C.

πr2h

D.

All of these

#### SOLUTION

Solution : C

A soda can is a rough example of a cylinder.

The volume of a cylinder is πr2h.
The capacity of any vessel is its internal volume so, the capacity of a soda can be calculated using the formula πr2h.

Where,
r = base radius of the can

h = height of the can

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

A.

True

B.

False

#### SOLUTION

Solution : B

Volume of cube = (edge)3
Hence the volume of cube with edge 24 m is (24)3
= 13824 m3.

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

A.

Hexagon

B.

Pentagon

C.

Cube

D.

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.

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

A.

is equal to

B.

is double of

C.

is three times of

D.

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=πr2hNew  radius=2rNew height=h2New volume=π(2r)2h2=2πr2hNew volume=2V

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 A.

28 cm

B.

32 cm

C.

24 cm

D.

20 cm

#### SOLUTION

Solution : A

The area of a trapezium is given by:
A=12×(Sum of parallel sides)×(height)
36=12×(12+6)×h
h=4 cm
So now in the trapezium,
h=4 cm
a=b=6 cm
AB=CD[S-A-S congruency inAFB and DEC]
2AB+a=12 cm
2AB=126
AB=CD=3 cm
So now inABF,AB2+h2=d2
d2=32+42=25
d=5 cm
As the trapezium is isosceles, the slant sides of the trapezium are equal in length
d=c=5 cm
the perimeter of the trapezium
=(2×AB)+a+c+b+d
=(2×3)+6+5+6+5=6+22=28 cm

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.