# Quantitative Aptitude: Mensuration Questions Set 3

Mensuration Questions SBI PO, NIACL, IBPS PO, NICl, LIC, Dena Bank PO PGDBF, BOI, Bank of Baroda and other competitive exams

1. A right circular cone is exactly fitted inside a cube in such a way that the edges of the base of the cone are touching the edge of one of the faces of the cube and the vertex is on the opposite face of the cube. If the volumes of cube is 216 cm3 , what is the volume of the cone (approximately)?
A) 56 cm3
B) 60 cm3
C) 46 cm3
D) 50 cm3
E) None of these
Option A
Solution
:

volume(a3)=216 , hence a=6
r= 3 cm; height of the cone= 6cm (as it is fitted in this cube of side 6 cm, hence its height will also be 6 cm)
Volume of cone= 1/3 π*r2 * h
=56
2. The diagram shows a section of a rocket firework. If this section can be completely filled with gunpowder what is the volume of gunpowder required?
A) 1882 cm3
B) 1782 cm3
C) 1982 cm3
D) 1682 cm3
E) None of these
Option B
Solution
:

sin 60 = P/H=r/6=√3/2
=> r=3√3 cm
In the cone; 62 = h2 + r2
h=3 cm
Volume of Gunpowder= Volume of Cone+ Volume of Cylinder=1/3 πr2h + πr2h = πr2 (1/3 h+h)
=22/7*27*21=1782
3. If a square, circle and rectangle has same perimeter then which one of them has the maximum area?
A) Square
B) Circle
C) Rectangle
D) All have equal area
E) Cannot be determined
Option B
Solution
: In such case the area in descending order is: Circle> Square> Rectangle
4. A cylinder has some water at height 20 cm. If a sphere of radius 6 cm is poured into it then find the rise in height of water if the radius of cylinder is 8 cm.
A) 3.5 cm
B) 9.5 cm
C) 4.5 cm
D) 5.5 cm
E) None of these
Option C
Solution
:

Volume of ball= volume of rising water in the cylinder

4/3 * π*r3 = π*r2 *h
4/3*6*6*6=8*8*h
h=4.5 cm
5. If the base of a pyramid is square and its side is 4√2 cm and slant height of pyramid is 5 cm, find the volume of pyramid.
A) 48 cm3
B) 16 cm3
C) 24 cm3
D) 32 cm3
E) None of these

Option D Solution:
l=slant height=5 cm ; h=height; side=4√2 cm
l2 = h2 + [(side*√2)/2]2
Note: The content inside bracket is the calculation for half of the diagonal of the square.
h= 3 cm
volume= 1/3 * Area of base * h
=1/3 * 32 * 3= 32
6. A sphere of 5 cm radius is melted and small sphere of radius 1 cm is made from it. Find the number of sphere that can be made from it.
A) 25
B) 125
C) 50
D) 100
E) None of these
Option B
Solution
: Number of sphere=Volume of large sphere/volume of small sphere
[4/3* π *r13 ]/ [4/3* π *r23 ]=5*5*5/1*1*1=125
7. A person wants to make a cylindrical box which is open from the top. If the height of that box is 10 cm and radius is 7 cm find the area of sheet which is required to make it.
A) 880 cm2
B) 1188 cm2
C) 594 cm2
D) 440 cm2
E) None of these
Option C
Solution
: Area required=Curved surface area + Area of base= 2 π r h + π r2 = 594
8. A square park has a 2 m wide cross road in middle of it. If the side of park is 100 m then find the remaining area of the park.
A) 9650 m2
B) 9596 m2
C) 9600 m2
D) 9604 m2
E) None of these
Option D
Solution
:
Total area= 10000
road area= 2*100 + 2*100- 2*2=396
remaining area=10000-396=9604
9. In a right circular cone the radius of its base is 6 cm and its height is 14 cm. A cross section is made through the mid-point of the height parallel to the base. The volume of the lower portion is?
A) 528 cm3
B) 366 cm3
C) 498 cm3
D) 462 cm3
E) None of these

Option D Solution:

Volume of cone= 1/3 π*r2 * h
Volume of lower part=volume of full cone-volume of upper cone
for full cone take r=6, h=14
for upper cone take r1=r/2=3 and h=7
volume of lower part=528-66=462
10. If radius of cone decrease by 50% and height increase by 20%. Then find the percentage change in the volume.A) 70% decrease
B) 70% increase
C) 40% decrease
D) 40% increase
E) 20% increase
Option A
Solution
:
Volume of cone= 1/3 π*r2 * h
r=50% dec =1/2 =>2————1
2———–1(dec)
h=20% inc =1/5 =>5————-6 (inc)
2*2*5:1*1*6=10:3
(3-10)/10*100=70% dec

## 10 Thoughts to “Quantitative Aptitude: Mensuration Questions Set 3”

1. Pulkit

thanks mam nice question 🙂

2. ?@shh...ishhh..⛷?

thnx

3. sachin shukla@ my turn 2017

ty

4. garima shah

how sphere will be poured into cylinder if sphere(r=6cm) has more radius than cylinder(r=4cm)

5. Nishu

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