BANK & INSURANCE (MENSURATION) PART 1

Total Questions: 60

51. The total area of a Square and rectangle is 496 Sq cm. The side of the square is 14 cm. What is the sum of the perimeter of square and rectangle, if length of the rectangle is 25 cm?

Correct Answer: (c) 130 cm
Solution:

a² + lb = 496
14² + 25b = 496
196 + 25b = 496
25b = 496 − 196
25b = 300
b = 12 cm

Perimeter of square = 4a = 4 × 14 = 56 cm
Perimeter of rectangle = 2 × (l + b) = 2 × (25 + 12)
=> 2 × 37 = 74 cm
Required sum = 56 + 74 = 130 cm

52. The perimeter of the rectangular field is 2 times the perimeter of square field. If the side of the square field is 18 m and the breadth of the rectangular field is 45 m, then find the area of the rectangular field?

Correct Answer: (a) 1215 Sq m
Solution:Side of square (a) = 18 m
Perimeter of rectangle = 2 × 4a = 2 × 4 × 18 = 144
=> 2(l + 45) = 144
=> l + 45 = 72
=> l = 72 − 45 = 27 m
Area of rectangle = l × b = 45 × 27 = 1215 Sq m.

53. The cost of fencing a square plot at the rate of Rs. 15 per meter is Rs. 3780. What will be the cost of flooring the plot at the rate of Rs. 3 per square meter?

Correct Answer: (d) 11907
Solution:Perimeter of square = 3780/15 = 252
4a = 252
Side (a) = 252/4 = 63
Area of square = a² = 63² = 3969
Cost of flooring the plot = 3979 × 3 = Rs. 11907

54. The circumference of a circle is equal to the perimeter of a square whose area is 4356 sq cm. What is the area of the circle?

Correct Answer: (b) 5544 Sq cm
Solution:

The circumference of a circle = Perimeter of a Square
Area of Square = a² = 4356
Side (a) = 66 cm
Perimeter of square = 4a = 66 × 4 = 264 cm
According to the question,
2πr = 264
2 × (22/7) × r = 264
r = 42

Area of the circle = πr² = (22/7) × 42 × 42 = 5544 Sq cm

55. Find the volume of a cylinder whose radius is one-third of the radius of a circle having area 1386 cm². Height of the cylinder is double its radius?

Correct Answer: (c) 2156 cm³
Solution:

πr² = 1386
=> (22/7) × r² = 1386
=> r² = 1386 × (7/22)
=> r² = 441
=> r = 21 cm

Radius of the cylinder = 21 × (1/3) = 7 cm
Height of the cylinder = 7 × 2 = 14 cm
Volume of the cylinder = πr²h = (22/7) × 7 × 7 × 14
= 2156 cm³

56. The side of the equilateral triangle is equal to the diameter of the circle. The area of the equilateral triangle is 196√3 Sq cm. Find the circumference of the circle?

Correct Answer: (b) 88 cm
Solution:

The area of the equilateral triangle = 196√3 Sq cm
The area of the equilateral triangle = (√3/4) × a²
(√3/4) × a² = 196√3
a² = 196 × 4
Side (a) = 14 × 2 = 28 cm
The diameter of the circle = 28 cm

Radius (r) = 14 cm
Circumference of the circle = 2πr = 2 × (22/7) × 14
= 88 cm

57. If the breadth of a parallelogram is increased by 30% while the height of the parallelogram is decreased by 20% then find percentage change in area of the parallelogram?

Correct Answer: (d) 4 % increased
Solution:

Let the breadth and height of the parallelogram is 10 cm and 10 cm,
Normal area = 10 × 10 = 100
New length = 10 × 130/100 = 13
New height = 10 × 80/100 = 8
New area = 13 × 8 = 104

Required percentage = [(104 − 100)/100] × 100
= 4 % increased

58. The circumference of a circle is half of the perimeter of a rectangle. The area of the circle is 2464 sq. m. What is the area of the rectangle if the breadth of the rectangle is 80 m?

Correct Answer: (a) 7680 Sq m
Solution:

Area of a circle = πr²
2464 = 22r²/7
2464 × (7/22) = r²
r² = 784
r = 28 m

Circumference = 2 × 22/7 × 28 = 176 sq. m
Perimeter of the rectangle = 2 × 176 = 352 sq. m

352 = 2(l + 80)
176 = l + 80
l = 176 − 80
l = 96

Area of the rectangle = 96 × 80 = 7680 sq. m

59. The radius of the circle is equal to two-fifth of the side of the square. The area of the circle is 616 sq cm. Find the perimeter of a square?

Correct Answer: (c) 140 cm
Solution:

Radius = (2/5) × side
Area of circle = πr² = 616
(22/7) × r² = 616
r² = 616 × (7/22) = 196
Radius (r) = 14 cm

Side = Radius × (5/2) = 14 × (5/2) = 35 cm
Perimeter of the square = 4a
=> 35 × 4
=> 140 cm

60. A Circular path is surrounding the circular plot is being graveled at a total cost of Rs. 3080 at Rs. 4 per square meter. Find the width of the path, if the radius of the circle is 14 m?

Correct Answer: (b) 7 meter
Solution:

Radius of the circular plot = 14 m
Area of the circular path = 3080/4 = 770

Area of the path = π[(r + x)² − r²] (Here x is the width of the path)
=> (22/7) [(14 + x)² − 14²]
=> (22/7) [196 + 28x + x² − 196]
=> (22/7) [28x + x²]
(22/7) [28x + x²] = 770
28x + x² = 770 × (7/22)
28x + x² = 245
x² + 28x − 245 = 0
(x + 35)(x − 7) = 0
x = 7 meter