Mensuration Model Questions Set 2 Practice Questions Answers Test with Solutions & More Shortcuts
Mensuration PRACTICE TEST [2 - EXERCISES]
Mensuration Model Questions Set 1
Mensuration Model Questions Set 2
Question : 16
A rectangle carboard is 18 cm × 10 cm. From the four corners of the rectangle, quarter circles of radius 4 cm are cut. What is the perimeter (approximate) of the remaining portion?
a) 51.0 cm
b) 47.1 cm
c) 49.1 cm
d) 53.0 cm
Answer »Answer: (c)
Remaining perimeter
= $({2 πr}/4)$4 + 10 + 2 + 10 + 2 = 2 × 3.14 × 4 + 24
= 25.12 + 24 = 49.12 cm
= 49.1 cm (approx)
Question : 17
In a Δ ABC, AD is the median through A and E is the mid– point of AD and BE produced meets AC at F. Then, AF is equal to
![mensuration area and volume aptitude mcq 22 107](https://careericons.com/adminicon/bunch/images/mensuration-area-and-volume-aptitude-mcq-22-107.png)
a) AC/ 3
b) AC/ 5
c) AC/ 4
d) AC/ 2
Answer »Answer: (a)
In ΔABC, we draw a line l || BF which intersect AC at G. In ΔADG and ΔAEF;
given that EA is the mid point of AD and DL || EF.
So, concept of similar triangle.
F is also mid point of AG. AF = FG (i)
DADG and DAEF are similar.
Again
ΔFBC and ΔDCl
BF || DG
given that AD is median so thad DB the mid point of BC.
G will be The mid point of CF
CG = GF ...(ii)
From equations (i) and (ii), we get
AF = FG = CG ...(iii)
From figure, AC = AF = FG + CG
= AF + AF + AF + 3AF
⇒ AF = $1/3$ AC
Question : 18
A cardboard sheet in the form of a circular sector of radius 30 cm and central angle 144º is folded to make a cone. What is the radius of the cone?
a) 21 cm
b) 12 cm
c) 18 cm
d) None of these
Answer »Answer: (b)
length of the are = 2 π r $(θ/{360º})$
Radius of arc(r) = 30 am
Length of the arc = 2πr = 2π × 30 × ${144}/{360}$ = 24π
Let the radius of the cone = R ∴ 2πR = 24π
⇒ R = ${30 × 144}/{360}$ = 12cm
Question : 19
Using the data in the above question, what is the breadth of the rectangle ?
a) 8
b) 6
c) 12
d) 10
Answer »Answer: (a)
Breadth of the rectangle is 8 units, as solved above
Question : 20
In the given triangle, AB is parallel to PQ. AP = c, PC = b, PQ = a, AB = x. What is the value of x?
a) $b + {ca}/b$
b) $a + {ab}/c$
c) $a + {bc}/a$
d) $a + {ac}/b$
Answer »Answer: (d)
In ΔABC and ΔPQC,
∴ ${PC}/{AC} = {PQ}/{AB}$
⇒ $b/{c + a} = a/x$
∴ x = ${a(c + b)}/b = {ac}/b + a$
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