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# Quant Quiz On Mensuration Day 26 Bag

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## Quant Quiz On Mensuration Day 26 Bag

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• The ratio between volumes of a hemisphere and a cone is 1:1. If the cone’s height is equal to its diameter, then find the ratio of diameter of hemisphere and cone ?
A) 2:1
B) 1:1
C) 3:2
D) 2:3
Option B
Solution:
let the radius of hemisphere and cone are r1 and r2
H’s volume/c’s volume = 1/1
So [2/3 πr13]/[1/3 πr22*2r2] = 1/1
So r1 : r2 = 1 : 2 or D1 : D2 = 1: 1
• If the height of a pyramid is 12cm and its base is a square which perimeter is 40cm, then find the volume of pyramid?
A) 300 cm³
B) 200 cm³
C) 400 cm³
D) 500 cm³
Option C
Solution:
perimeter of base =40
Side of base = 10
Area of base = 100
Volume = 1/3 * area of base * height
= 1/3 * 100 * 12 = 400cm³
• If the perimeter of square, circle, rectangle, are equal. Then whose area is largest?
A) Circle
B) Square
C) Rectangle
D) All are equal
Option A
Solution:
when perimeter of these are equal then descending order of area is
Circle >square> rectangle.
So option A is Ans
• A rectangular plot of grass is 50m long and 40m broad. From the center of each side a path of 3m wide goes across the center of the opposite side. Find the area of path?
A) 270
B) 280
C) 251
D) 261
Option D
Solution:

area of road = 3*50 + 3*40 −3²
= 270 −9=261

• The height of the cone is 24 cm and the curved surface area of cone is 550 cm2. Find its volume.
A) 1200 cm2
B) 1232 cm2
C) 1240 cm2
D) 1260 cm2
E) 1262 cm2
Option B
Solution
:
Volume= 1/3 π*r2 * h
Answer will be divisible by 11, as in pie we have 2*11. As only 1232 is divisible by 11, it is the answer
• The side of a square base of a pyramid increases by 20% and its slant height increases by 10%. Find the per cent change in Curved Surface Area.
A) 28%
B) 58.4%
C) 32%
D) 45.20%
E) 48%
Option C
Solution
:
C.S.A=1/2*(perimeter of base)*l
20+10+(20*10)/100=32%
• If a copper wire is bend to make a square whose area is 324 cm2. If the same wire is bent to form a semicircle, then find the radius of semicircle.
A) 7 cm
B) 14 cm
C) 11 cm
D) 21 cm
E) 12 cm
Option B
Solution
:
Area of square= 324, hence side =18
Perimeter = 4a =4*18=72
Circumference of semicircle= 2r+Pie *r
r(2+pie)=72
r=14 cm
• A man wants to make small sphere of size 1 cm of radius from a large sphere of size of 6 cm of radius. Find out how many such sphere can be made?
A) 216
B) 125
C) 36
D) 200
E) 64
Option A
Solution
:
Volume of sphere1/volume of sphere 2= required number of sphere
=6*6*6/1*1*1=216
• A sphere of radius 9 cm is dip into a cylinder who is filled with water upto 20 cm. If the radius of cylinder is 6 cm find the percentage change in height.
A) 50%
B) 40%
C) 55%
D) 45%
E) 57%
Option D
Solution
:
Volume of sphere= volume of cylinder from height 20 cm to upwards.
4/3 * π * 9*9*9 = π * 6*6*h
h=9
new height=20+9=29
%change= 9/20*100=45%
• The length of the perpendicular drawn from any point in the interior of an equilateral triangle to the respective sides are P1, P2 and P3. Find the length of each side of the triangle.
A) 2/√3 *(P1 + P2 + P3)
B) 1/3 * (P1 + P2 + P3)
C) 1/√3 *(P1 + P2 + P3)
D) 4/√3 *(P1 + P2 + P3)
E) 5/√3 *(P1 + P2 + P3)
Option A
• A conical cup is filled with ice cream. The ice cream forms a hemispherical shape on its top. The height of the hemispherical part is 7 cm. The radius of the hemispherical part equals the height of cone then the volume of ice cream is?
A) 1078 cm3
B) 1708 cm3
C) 7108 cm3
D) 7180 cm3
E) 1808 cm3
Option A
Solution
:
Volume = volume of hemisphere + volume of cone= 2/3* π *r3 + 1/3 π * r2 *h
=1078
• Assume that a drop of water is spherical and its diameter is one tenth of a cm. A conical glass has equal height to its diameter of rim. If 2048000 drops of water fill the glass completely then find the height of the glass.
A) 12 cm
B) 16 cm
C) 20 cm
D) 8 cm
E) 10 cm
Option B
Solution
:
diameter of drop of water=1/10 => radius=1/20
volume of 204800 drop of water=204800*4/3* π*1/20 *1/20*1/20 = 1024 π/3
Volume of cone=1024 π/3 = 1/3 * π *r2 * h (r=h/2)
h=16
• If the radius of a sphere increase by 4 cm then the surface area increase by 704 cm2 . The radius of the sphere initially was?
A) 5
B) 4
C) 6
D) 8
E) 10
Option A
Solution
:
4 π(r+4)2 – 4 * π*r2 = 704
solve and get r=5
• By melting two solid metallic spheres of radii 1 cm and 6 cm, a hollow sphere of thickness 1 cm is made. The external radius of the hollow sphere will be.
A) 8 cm
B) 9 cm
C) 6 cm
D) 7 cm
E) 10 cm
Option B
Solution
:
4/3* π (R3 + r3)= 4/3* π * ((x+1)3 – x3)
R=6 cm; r=1 cm; x= radius of hollow sphere inner; (x+1)=outer radius
solve and get x=8
outer=x+1=9 cm

• 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
• 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 + r
h=3 cm
Volume of Gunpowder= Volume of Cone+ Volume of Cylinder=1/3 πr2h + πr2h = πr(1/3 h+h)
=22/7*27*21=1782
• 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
• 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 4 cm.
A) 3 cm
B) 9 cm
C) 18 cm
D) 15 cm
E) None of these
Option C
Solution
:

Volume of ball= volume of rising water in the cylinder
4/3 * π*r= π*r*h
4/3*6*6*6=4*4*h
h=18 cm
• 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
l= 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
• 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 *r1]/ [4/3* π *r23 ]=5*5*5/1*1*1=125
• 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
• 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
• 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
• 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