# Quantitative Aptitude: Mensuration Questions Set 16

1. If the length of a rectangular field is increased by 15% and breadth is also increased by 10%, the area of the rectangle will be 253 m^2. What is the area of the original area of rectangle ?
400
240
350
180
200
Option E
let original area of rectangle =100
percentage change in area=15+10+15*10/100=26.5
126.5=253
original area=253/126.5*100=200 m^2

2. The side of square is 25% more than the length of rectangular and perimeter of square is 80cm. Ratio of length and breadth of rectangular is 4:3, then find the area of rectangular.
192
215
180
220
240
Option A
let the length of rectangular=4x
side of square=5x
perimeter of square=5x*4=20x
20x=80
x=4
length of rectangular=4*4=16
area of rectangular=16*12=192 cm^2

3. The area of square 50m^2 less than the area of a rectangular, whose breadth is 12m. If the perimeter of a square is 40m, then find the perimeter of a rectangular.
50
49
60
65
70
Option B
perimeter of square=40
side of square=40/4=10m
area of square=10^2=100
area of rectangular=100+50=150m^2
length=150/12=12.5m
perimeter=2(12.5+12)=49

4. The area of the square is in the ratio of 1444:1296. What will be the ratio of their perimeter ?
20:21
19:18
22:25
23:24
18:19
Option B
The ratio of area= 1444:1296
a^2:b^2=38:36=19:18
ratio of their perimeter=19*4:18*4=19:18

5. The side of square is 5cm more than the radius of a circle. The area of the circle is 154cm^2. What is the perimeter of the square ?
44
64
56
48
52
Option D
area of the circle=154cm^2
πr^2=154
r^2=49
r=7
side of square=7+5=12cm
perimeter of square=12*4=48cm

6. The length of rectangular is 18cm which is 4cm more than diameter of a circle. What is the area of the circle ?
154
240
150
176
198
Option A
diameter of circle=18-4=14
2r=14
r=7
area of the circle=πr^2=22/7*7*7=154cm^2

7. There is a rectangular field of 40cm in length and 30cm in breadth. On the inside of which a 5cm wide road, then find the area of road.
800
500
700
600
1000
Option D
area of the outside rectangular field=40*30=1200cm^2
length of inside rectangular=40-10=30
area of the inside rectangular=30*20=600

8. The height and radius of a cylinder is 21cm and 12cm respectively. Find the volume of cone.
4268
3168
4360
4530
4840
Option B
height of the cylinder=21cm
volume of the cylinder=22/7*12*12*21=22*144*3
volume of the cone=1/3*volume of cylinder
=1/3*22*144*3=3168cm^2

9. The ratio of the length of the diagonals of a rhombus is 4:3. If the perimeter of the rhombus is 160m. What is the length of the diagonal of a square whose area is same as that of rhombus ?
15√3
16√3
20√2
25√5
24√2
Option B
let the diagonals of the rhombus be 4x and 3x
side length of the rhombus=√(4x)^2+(3x)^2
=√16x^2+9x^2
=25x^2=5x
perimeter=4*5x=20x=160
20x=160
x=8
two diagonal of the rhombus=32 and 24
area=1/2*32*24=384
let the diagonal of the square=D
side of the square=D/√2
(D/√2)^2=384
D^2/2=384
D=16√3

10. The circumference of the circle is 176cm and the radius of circle is 4 less than side of the square. Find the area of the square.
576
1000
784
1024
1444
Option D
2πr=176
r=176*7/44=28
side of square=28+4=32
area of square=32*32=1024