MENSURATION (SSC, MBA, CDS)

#MENSURATION#
Here we are creating question sample from Mensuration that are important for IBPS, SBI, RBI, SSC, LIC and other competitive exams. We have included some questions that are repeatedly asked in exams !!
1.A circular wire of radius 56 cm is cut and bent in the form of a rectangle whose sides are in the ratio of 6:5. The smaller side of the rectangle is
A.70cm
B.75cm
C.80cm
D.85cm
E.None of these
Answer & Explanation
Answer – C.80cm
Explanation :
The perimeter of the circle, that is, the rectangle is,
P=2πr = 2 * 22/7 * 56 =16×22 cm.
Let us assume the actual length and breadth of the rectangle be, 6xand 5x
So perimeter will be,
P=2(6x+5x)=22x
16×22=22x
X=16.
The smaller side or breadth =5x=80cm
2.The circumference of a circle is twice the perimeter of a rectangle. The area of the circle is 5544sq cm. What is the area of the rectangle if the length of the rectangle is 30cm ?
A.850sq cm
B.990sq cm
C.1080sq cm
D.1150sq cm
E.None of these
Answer & Explanation
Answer – C.1080sq cm
Explanation :
Area of circle = (22/7)*r2
5544 = (22/7)*r2
r2= 5544*7/22
r = 42
circumference of the circle = 2*(22/7)*42 = 264cm
perimeter of the rectangle = 2(30+b)
264/2 = 60+2b
132 = 60+2b
2b = 72
b = 36cm
Area of the rectangle = 36*30 = 1080sq cm
3.The ratio between the perimeter and the breadth of a rectangle is 5:1. If the area of the rectangle is 294 square cm, what is the length of the rectangle?
A.12 cm
B.15 cm
C.19 cm
D.21 cm
E.None of these
Answer & Explanation
Answer – D.21 cm
Explanation :
Perimeter=2*(l+b)
Perimeter/breadth = 5/1
2*(l+b)/b = 5/1
2l+2b = 5b
l= 3/2 b.
Area =l*b= 294 sq. units.
3/2 * b2 = 294
b=14
l= 21
4.A rectangular sheet of metal is 40cm by 15cm. Equal squares of side 5cm are cut off at the corners and the remainder is folded up to form an open rectangular box. The volume of the box is
A.750cm3
B.720cm3
C.680cm3
D.650cm3
E.None of these
Answer & Explanation
Answer – A.750cm3
Explanation :
Length of rectangular sheet = 40 cm
Breadth of rectangular sheet = 15 cm
Since, squares of side 5 cm are cut off from the corner of the sheet.
Therefore, new length = 40 – (5 + 5) cm = 30 cm
new breadth = 15 – (5 + 5) cm = 5 cm
Now, volume of the open box = (30 × 5 × 5) cm3 = 750 cm3
5.10 cylindrical pillars of a building have to be painted. The diameter of each pillar is 70 cm and the height is 4m. What is the cost of painting at the rate of Rs. 10 per square metre?
A.790
B.850
C.880
D.920
E.None of the Above
Answer & Explanation
Answer –C.880
Explanation :
CSA of 10 cyc= 10*2πrh
= 2 * 22/7 * 35/100 * 4
= 44*35*4/(700)
= 10*176*35/700
= 176*35 /70
Cost = 10*176*35/70
= 880rs
6.In a rectangle the ratio of the length and breadth is 3:2. If each of the length and breadth is increased by 4m their ratio becomes 10:7. The area of the original rectangle in m² is?
A.384
B.486
C.546
D.864
E.None of the Above
Answer & Explanation
Answer – D.864
Explanation :
[3x + 4 / 2x + 4] = 10/ 7
x = 12
Area of the original rectangle = 3x * 2x = 6x²
Area of the original rectangle = 6 * 144 = 864 m²
7.The length of a rectangular plot is 10 metres more than its breadth. If the cost of fencing the plot @ 26.50 per metre is Rs. 5300, what is the length of the plot in metres?
A.50
B.55
C.60
D.65
E.None of the Above
Answer & Explanation
Answer – B.55
Explanation :
Let breadth = x metres.
Then, length = (x + 20) metres.
Perimeter = 5300/26.50 = 200m
2[(x + 10) + x] = 200
x = 45.
Hence, length = x + 10 = 55 m.
8.A tank is 25 m long, 12 m wide and 6 m deep. The cost of plastering its walls and bottom at 25paise per sq. m, is:
A.212
B.195
C.186
D.174
E.None of the Above
Answer & Explanation
Answer – C.186
Explanation :
Area to be plastered = [2(l + b) x h] + (l x b)
Area= {[2(25 + 12) x 6] + (25 x 12)} = 744 m2
Cost of plastering = 744 * 25/100 = 186
9.A rectangular field is to be fenced on three sides leaving a side of 30 feet uncovered. If the area of the field is 720 sq. feet, how many feet of fencing will be required?
A.65
B.78
C.82
D.89
E.None of the Above
Answer & Explanation
Answer – B.78
Explanation :
L = 30; lb = 720;
B= 24 ft
Length of fencing = l + 2b = 30 + 48 = 78 ft
10.The perimeter of a rectangular field is 120 m and the difference between its two adjacent sides is 40 m. The sides of the square field whose area is equal to this rectangular field is?
A.15√3
B.10√3
C.15√5
D.10√5
E.None of the Above
Answer & Explanation
Answer – D.10√5
Explanation :
Perimeter of rectangle = 2(l + b) = 120
l + b = 60m — (1)
l – b = 40m –(2)
From (1) and (2)
l = 50 m; b = 10m
Area of rectangle = 500m² = Area of Square
Side of a square = 10√5
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