# Quantitative Aptitude: Mensuration Questions Set 9

1. The ratio between the perimeter and the breadth of a rectangle is 26 : 5. If the area of the rectangle is 1000 sq. cm, what is the length of the rectangle?
45cm
35cm
40cm
30cm
None
Option C
Solution:
2(l+b):b=26:5
10l+10b=26b
10l=16b
b=5/8l
Area lb=1000
l*5/8l=1000
l2=1600
l=40cm.
2. A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:
49m2
53m2
38m2
40m2
None
Option A
Solution:
Area=[2(lb+bh+hl)-lb] =2(bh+hl)+lb
=[2(4*1.25 + 6*1.25) + (6*4)] =25+24
=49m2.
3. The radius of the base of a cylindrical Can is 140cm and its height is 240cm. It is full of Petrol. How many tins, each of size 25 cm × 22 cm × 30 cm can be filled with Petrol from the Can?
896
784
852
926
None
Option A
Solution:
Volume of Can=(22/7)*140*140*240
=22*20*140*240
Volume of a tin=25*22*30
Number of tins=(22*20*140*240)/(25*22*30)
=4*8*28=896.
4. The length of a room is 6.5 m and width is 2.75 m. Find the cost of paying the floor by slabs at the rate of Rs. 400 per sq.metre.
Rs7350
Rs6100
Rs7150
Rs6450
None
Option C
Solution:
Area = 6.5 * 2.75
Cost for 1 sq. metre. = Rs. 400
Total cost = 6.5 * 2.75 * 400
=Rs7150.
5. The ratio of the radius and height of a cone is 7: 18. Its volume is 924 cm. Its radius and height is
14cm, 36cm
21cm, 54cm
7cm, 18cm
28cm, 72cm
None
Option C
Solution:
Volume of cone 1/3*22/7*7x*7x*18x=92
22*6*7x=924
x=1.
Then r=7, h=18.
6. The diagonal of a rectangle is √125 cm and its area is 50 sq. cm. The perimeter of the rectangle must be:
45cm
30cm
42cm
36cm
None
Option B
Solution:
√(l2 + b2)=√125
lb=50
(l+b)2=l2=+b2=+2lb
=125+(2*50)
=225.
L+b=15
Perimeter=2*15=30cm.
7. A rectangular block of metal has dimensions 21 cm*77 cm*24 cm. The block has been melted into a sphere. The radius of the sphere is
28cm
21cm
32cm
18cm
None
Option B
Solution:
Volume of the sphere=4/3*22/7*r3
4/3*22/7*r3=21*77*24
r3=(21*77*24*3*7)/(4*22)
=33 * 73
r=3*7=21cm.
8. The perimeter of a square is equal to twice the perimeter of a rectangle of length of 8 cm and breadth 7 cm. What is the circumference of a semicircle whose diameter is equal to the side of the square?
34.6cm
36cm
38cm
38.5cm
None
Option D
Solution:
Perimeter of rectangle = 2(l+b) = 2(8+7)= 30cm
Perimeter of square is twice the perimeter of rectangle = 2*30= 60cm
Then, side of the square is = 1/4 x 60 = 15cm.
Circumference of the semicircle =πr + 2r
=22/7*15/2 +2*15/2
=23.5+15
=38.5cm.
9. Surface area of a cube is 2400 cm 2. Find out the length of its diagonal.
16√3cm
20√3cm
24√3cm
26√3cm
None
Option B
Solution:
Surface area of cube 6*side2
6*side2=2400
side2=2400/6=400
side=20cm.
Diagonal of cube=√3*side=20√3cm.
10. The radius of a circular field is equal to the side of a square field. If the difference between the perimeter of the circular field and that of the square field is 48m, what is the side of the square field?
26m
31m
24m
21m
None
Option D
Solution:
Radius of circular field=side of square field
2*22/7a – 4a=48
(44-28)a=(48*7)
16a=48*7
a=21m.