# Quantitative Aptitude: Mensuration Questions Set 15

1. The ratio of length and breadth of rectangular field is 3 : 2. If the perimeter of rectangular field is 40cm, then what is the area of square whose side 5cm more than the length of rectangular field ?
216
289
324
196
400
Option B
Let length and breadth or rectangular field = 3x and 2x
perimeter = 40
2(3x + 2x) = 40
10x = 40
x = 4
length = 3 * 4 = 12cm
side of square = 12 + 5 = 17
Area of square = 17 * 17 = 289 cm^2

2. Length of two rectangles A and B is 14 cm and 20 cm respectively and sum of their breadth 14 cm. If ratio of perimeter of A and B is 5 : 7, then what is the difference between area of these rectangles ?
84
54
42
62
76
Option E
Let breadth of rectangular A = x
and breadth rectangular B = 14 – x
perimeter of rectangular A = 2 (14 + x)
perimeter of rectangle B = 2 (20 + 14 – x)
= 2 (34 – x)
2 (14 + x)/2 (34 – x) = 5/7
340 – 10x = 196 + 14x
x = 6
breadth of rectangle A = 6 cm
breadth of rectangle B = 14 – 6 = 8 cm
Area of rectangle A = 14 * 6 = 84 cm^2
Area of rectangle B = 20 * 8 = 160 cm^2
Difference = 160 – 84 = 76 cm^2

3. If the diagonal of a cube is of length ‘x’, then what is the lateral surface area of that cube ?
2x^2/3
5x/3
4x/3
4x^2/3
8x
Option D
Diagonal of cube = aâˆš3
aâˆš3 = x
a = x/âˆš3
lateral surface area = 4a^2 = 4*(x/âˆš3)^2 = 4x^2/3

4. If the total surface area of a cube is 8664 cm^2, the what is the length of its diagonal ?
46âˆš3
34âˆš3
38âˆš3
24âˆš3
19âˆš2
Option C
T.S.A = 8664
6a^2 = 8664
a^2 = 1444
a = 38
diagonal = aâˆš3 = 38âˆš3

5. If the ratio of radius of two spheres A and B is 3 : 5, then what is the ratio of their volumes ?
27 : 125
3 : 5
12 : 25
9 : 25
6 : 15
Option A
Ratio of volume of A and B = 4/3Ï€(3)^3 : 4/3Ï€(5)^3
= 27 : 125

6. The ratio of length and breadth of rectangles is 5 : 3 and its area is 240 m^2. If the perimeter of square is 8m less than the perimeter of rectangles, then what is the area of square ?
324
196
1024
1444
1296
Option B
Let length and breadth of rectangles = 5x and 3x
Area = 240
15x^2 = 240
x = 4
length = 5 * 4 = 20
breadth = 3 * 4 = 12
perimeter of rectangle = 2 (20+ 12) = 64
perimeter of square = 64 – 8 = 56
side of square = 56/4 = 14
Area of square = 14 * 14 = 196

7. The non – parallel sides of a trapezium are equal to side of perimeter of square 40cm and the parallel sides are 8cm and 20cm respectively, find the perimeter of trapezium ?
38
24
20
36
40
Option D
perimeter of square = 40
side of square = 40/4 = 10cm
non-parallel side of trapezium = 10
one parallel side = 8cm
other parallel side = 20cm
breadth of tringle = 20 – 8/2 = 6
let height of trapezium = h
10^2 = h^2 + 6^2
h^2 = 64
h = 8
perimeter = 10 + 10 + 8 + 8 = 36 cm

8. The circumference of a circle A is equal to the perimeter of a square whose area is 1936 m^2. Diameter of circle B is four times the radius of circle A what is the area of circle B ?
4532
3952
2840
4900
9856
Option E
Area of square = 1936 m^2
side of square = âˆš1936 = 44m
perimeter of square = 44 * 4 = 176m
2Ï€r = 176
r = 176 *7 /44 = 28
diameter of circle B = 28 * 4 = 112
Area = Ï€r^2 = 22/7 * 56 * 56 = 9856

9. If the height and radius of a cylinder increased by 25% and 20% respectively. Then what is the change in percent in its curved surface area ?
20%
50%
40%
25%
58%
Option B
Let the height of cylinder = 4h
increased height = 4h* 125/100 = 5h
and radius of cylinder = 5r
increased radius = 5r * 120/100 = 6r
initial curved surface area = 2 * Ï€ * 4h * 5r = 40Ï€hr
new curved surface area = 2 * Ï€ * 5h * 6r = 60Ï€hr
% change = 60Ï€hr – 40Ï€hr/40Ï€hr * 100 = 50%

10. The length , breadth and height of a cuboid is 14m, 15m, 20m respectively,. Find the lateral surface area of cuboid ?
1225
1160
4250
2420
3840
Option B
L.S.A = 2 * 20 (14 + 15) = 40 * 29 = 1160 m