 # Quantitative Aptitude: Mensuration Questions Set 14

1. The perimeter of an equilateral triangle is equal to the perimeter of a square whose diagonal is 9√2 cm. Find out the area of the equilateral triangle ?
48√3
60√3
30√3
36√3
20√3
Option D
side of square=9√2/√2=9
let the side of equilateral triangle be x cm.
3x=4*9
x=12
area of equilateral triangle= √3/4*12*12=36√3

2. If ratio of height and radius of a cone is 5:6. Volume of cone is 480π cm^3, then find slant height of cone (in cm) ?
2√61
4√61
8√50
9√68
10√52
Option A
let height and radius of cone be 5x and 6x.
volume of cone =480π
1/3*π*6x^2*5x=480π
x^3=8
x=2 cm
so, slant height of cone =√(r^2+h^2)
= √(144+100)=√244=2√61

3. Circumference of a circle A is 2 times perimeter of a square. Area of the square is 484 cm^2. What is the area of another circle B whose radius is half the radius of the circle A ?
530
640
590
616
none of these
Option D
Area of the square =484cm
side of square =22cm.
perimeter of square =22*4=88cm.
ATQ,
circumference of a circle A=88*2 =176cm.
2πr =176
r=176*7/44 =28
Radius of circle B= 28/2 =14cm.
Area of circle B=22/7*14*14 =616cm^2

4. If the length of a rectangular field is increased by 20% and the breadth is reduced by 20%, the area of the rectangle will be 288 m^2 . What is the area of the original rectangle ?
400
300
520
220
none of these
Option B
Percentage change in area =
+20-20-(20*20)/100 =-4%
96%= 288
100%=288/96*100= 300 m^2

5. Side of a rhombus is 20cm and the ratio of diagonals of a rhombus is 3:4, then find the area of the rhombus .
384
264
544
288
484
Option A
Side of rhombus =20cm.
Let,
two diagonals of a rhombus be 3x and 4x.
side =√(3x)^2+(4x)^2
= 9x^2+16x^2 =5x
5x=20
x=4
two diagonals =(4*3*2) and (4*4*2) =24 and 32
Area =1/2*24*32 =384 cm^2.

6. The side of a square is 20% more than the side of an equilateral triangle whose perimeter is 75m. Find the ratio between perimeter of square to area of triangle.
96:125√3
48:55√3
32:58
96:130√3
32:42
Option A
perimeter of triangle=75
side of triangle=75/3=25m
side of square=25*120/100=30 m
perimeter of square=4*30=120 m
area of triangle=√3/4*25*25=625√3/4 m^2
ratio=120:625√3/4=480:625√3=96:125√3

7. Radius of circular field is 40% more than length of a rectangular field, having the area 80 m^2. If circumference of a circle is 88m, then radius of circular field is what percent more than breadth of rectangular field ?
60
50
120
75
100
Option D
and length of rectangular field=10m
area of rectangular field=80 m^2
required percentage=14-8?8*100=6/8*100=75%

8. Perimeter of a circle is 88cm. Find volume of a cylindrical vessel whose radius is equal to the radius of circle and height of cylindrical vessel is 20 cm.
15000
12320
14220
16780
20400
Option B
Perimeter of circle =88
r=88*7/44=14 cm
radius of cylindrical vessel =22/7*14*14*20 = 12320 cm^2

9. The ratio between length and breadth of a rectangular field is 5:4 . If area of rectangular field is 320 m^2, then find the perimeter of rectangular field.
64
40
100
72
84
Option D
Let length of field =5x
ATQ,
5x*4x =320
20x^2=320
x^2 =320/20 =16
x=4
Perimeter =2(5x+4x) =18x =18*4= 72

10. The total area of a circle and a square is equal to 1241 cm^2. The diameter of the circle is 28cm. What is the sum of the circumference of the circle and the perimeter of the square ?
132
188
192
288
196
Option B
diameter of circle=28cm
area of circle=22/7*14*14=616
ATQ,πr^2+a^2=1241
a^2=1241-616=625
a=25
circumference of the circle=2*22/7*14=88
perimeter of square=4a=4*25=100
sum=88+100=188

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