Mensuration Model Questions Set 2 Practice Questions Answers Test with Solutions & More Shortcuts

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: (c)

mensuration-area-and-volume-aptitude-mcq

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

a) AC/ 3

b) AC/ 5

c) AC/ 4

d) AC/ 2

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: (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: (a)

Breadth of the rectangle is 8 units, as solved above

Question : 20

mensuration-area-and-volume-aptitude-mcq
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: (d)

In ΔABC and ΔPQC,

mensuration-area-and-volume-aptitude-mcq

∴ ${PC}/{AC} = {PQ}/{AB}$

⇒ $b/{c + a} = a/x$

∴ x = ${a(c + b)}/b = {ac}/b + a$

IMPORTANT quantitative aptitude EXERCISES

Mensuration Model Questions Set 2 Online Quiz

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