# Quantitative Aptitude: Mensuration Questions Set 10

1. The side of the square exceeds the side of another square by 6cm and the sum of the areas of the two squares is 260cm2. The dimensions of the squares is
6cm and 12cm
8cm and 14 cm
10cm and 16cm
5cm and 11cm
None
Option B
Solution:
Let the side of the square=x cm
Side of another square = x+6 cm
x2 + (x+6)2 =260
x2 +6x -112=0
x=-14, 8(negative value neglected)
x=8cm.
Another square 8+6=14cm.
2. A lawn is in the shape of rectangle of length 30m and width 20m inside the lawn there is a footpath of uniform width 2m bordering the lawn. The area of the path is.
142m2
154m2
165m2
184m2
None
Option D
Solution:
Area of the outer rectangle=30*20
=600m2.
Width of path is 2m.
Inner length=30-4=26m
Inner rectangle area=26*16
=416m2.
Then Area of the path =600-416
=184m2.
3. The diameter of the wheel of a car is 140cm. Then, in order to keep the speed of 66km/hr. How many revolutions per minute must the wheel make?
250
180
220
195
None
Option A
Solution:
Circumference=2*22/7*0.7
=4.4m
Distance to be covered in 1 min =(66*1000)/60
=1100m.
Then no of revolutions per minute=1100/4.4
=250.
4. The length and breadth of a rectangular park are in the ratio 7:3. A path, 2.5m wide running all around the outside of the park has an area of 275m2. The dimensions of the park
28m, 12m
21m, 9m
35m, 15m
56m, 24m
None
Option C
Solution:
Area of the park =7x *3x=21x2
Length including the path =7x+5
Area=(7x+5) * (3x+5)
=21x2 +50x+25
Now, 21x2 +50x+25-21x2 =275
50x=250
x=5.
Then l=7*5=35m
B=3*5=15m.
5. Two circle touch externally. The sum of their areas is 169π and the distance between their centres is 17cm. The radius of the circles are
10cm, 4cm
12cm, 5cm
15cm, 8cm
8cm, 4cm
None
Option B
Solution:
Let the radius of the circles be x, 17-x
Sum of the area = π x2 + π(17-x) 2
π x2 + π(17-x) 2=169π
2πx2-34πx+120π=0
x2-17x+60=0
x=12 or 5.
6. A metallic sheet is of rectangular shape with dimensions 45cm *32cm from each of its corners a square of 5cm is cut off. An open box is made of the remaining sheet. What is the volume of the box?
3360cm3
2850cm3
2560cm3
3850cm3
None
Option D
Solution:
L=45cm
B=32cm
Square of side 5cm is cut off from each corner
Then length= 45 –(5+5)=35cm
And height of the box=5cm.
Volume of the box=35*22*5
=3850cm3.
7. The radius and the height of a right circular cone are in the ratio 5:12. If its volume is 314m3, the slant height and the radius are
13m
21m
18m
24m
None
Option A
Solution:
r=5x and h=12x
Volume of the cone=314 =1/3πr2h
1/3*3.14 *5x2*12x=314
314x3=314
x=1.
Then r=5m h=12m
Slant height=√(r2 +h2)
=√(25+144)
=√169=13m.
8. A 8cm cube is cut into 2cm cubes. What is the ratio of surface area of small cubes to that of the large cube?
3:2
4:3
4:1
5:2
None
Option C
Solution:
No of small cubes= Volume of large cube/volume of a small cube
=83/23
=64.
Total surface area of large cube=6*82=384cm2
Total surface area of 1 small cube=6*22=24cm2
Total surface area of 64 small cube=64*24=1536cm2
Ratio 1536:384
=4:1.
9. The area of a rectangle is 72 m2 and its length is 2 times is breadth. What is the perimeter of the rectangle?
42m
36m
30m
None
Option B
Solution:
Then
x*2x=72
x = 6 m
then l=12m and b=6m
Perimeter=2(12+6)
=36m.
10. The length of a rectangular floor is twice its breadth. If Rs.450 is required to paint the floor at the rate of Rs.1 per square metre, then what would be the length of floor?
28m
34m
26m
30m
None
Option D
Solution:
To paint per square metre for Rs 1.
Then 450m2 is the area of the floor.