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.
⇒6x×5x=750
⇒30x2=750
⇒x2=75030=25
⇒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 cmArea 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
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 πr
Perimeter=πr+2×Slant height
=227×1.4+2×2
⇒4.4+4=8.4cm
Question 4
PQRS is a quadrilateral in which PQ=5√2cm, QR=5√2cm, RS=8cm, SP=6cm, ∠PSR=∠PQR=90∘. Then its area is
40.4 cm2
46.4 cm2
32.4 cm2
49 cm2
SOLUTION
Solution : D
Area of right angled triangle ΔPQR
=12×Base×Height=12×5√2×5√2=25 cm2Area of right angled triangle ΔPSR
=12×8×6=24 cm2Area of quadrilateral PQRS
= Area of ΔPQR+ΔPSR=49 cm2
Question 5
The capacity of a soda can be calculated using the formula.
2πr(r+h)
2πr
πr2h
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 canh = 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 = (edge)3
Hence the volume of cube with edge 24 m is (24)3
= 13824 m3.
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
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=πr2hNew radius=2rNew height=h2New volume=π(2r)2h2=2πr2hNew volume=2V
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=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 in△AFB and △DEC]
∴2AB+a=12 cm
⇒2AB=12−6
⇒AB=CD=3 cm
So now in△ABF,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
Question 10
Every quadrilateral has two pairs of parallel sides.
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.