BANK & INSURANCE (MENSURATION) PART 1

Total Questions: 60

41. If the length of the rectangle increased by 25% and the breadth of the rectangle is decreased by 10%, then find the area of the rectangle will be increased or decreased?

Correct Answer: (b) 12.5% increased
Solution:

Original area of rectangle = 100
New area = 100 × 125/100 × 90/100 = 112.5
Area of rectangle is 12.5% increased

42. The length of the rectangle is 50% more than its breadth and the area of the rectangle is 1176 cm². If the perimeter of the rectangle is 5x cm and the side of the square is x cm, then find the perimeter of the square?

Correct Answer: (c) 112 cm
Solution:

Breadth of the rectangle = 2a
Length of the rectangle = 150/100 × 2a = 3a
2a × 3a = 1176
a = 14 cm

Perimeter of the rectangle = 2 × (42 + 28) = 140 cm
Side of the square = 140/5 = 28 cm
Perimeter of the square = 4 × 28 = 112 cm

43. Perimeter of the square is 48 cm and the side of the square is 75% of the length of the rectangle whose perimeter is equal to the perimeter of the square. What is the area of the rectangle?

Correct Answer: (d) 128 cm²
Solution:

4a = 48
a = 12 cm
Length of the rectangle = 4/3 × 12 = 16 cm
Breadth of the rectangle = 48/2 − 16 = 8 cm
Area of the rectangle = 16 × 8 = 128 cm²

44. The circumference of the semi-circle is 360 cm. If the side of the square is 3/5th of diameter of the semi-circle, then what is the perimeter of the square?

Correct Answer: (b) 336 cm
Solution:Circumference of the semi-circle = 360 cm
π(r + 2) = 360
π(22/7 + 2) = 360
Therefore, radius of the semi-circle = 70 cm
Diameter of the semi-circle = 140 cm
Side of the square = 3/5 × (140) = 84 cm
Perimeter of the square = 4a = 4 × 84 = 336 cm

45. If the ratio of length, breadth and height of a cuboid is 3:2:5 and the total surface area of the cuboid is 248 cm² and the length of the cuboid is equal to the breadth of the rectangle and length of the rectangle is 4 cm more than its breadth, then find the area of the rectangle?

Correct Answer: (a) 60 cm²
Solution:

248 = 2 × (3x × 2x + 2x × 5x + 5x × 3x)
31x² = 124
x² = 4
x = 2

Breadth of the rectangle = 2 × 3 = 6 cm
Length of the rectangle = 6 + 4 = 10 cm
Area of the rectangle = 6 × 10 = 60 cm²

46. Total surface area (in cm²) of a cube is 75% of volume (in cm³) of that cube. Find the total surface area of the cube?

Correct Answer: (b) 384 cm²
Solution:

Let side of the cube = ‘a’ cm
So, total surface area of the cube = 6a² cm²
And volume of the cube = a³ cm³

From the question:
6a² = a³ × (75/100)
6a² = 3a³/4
a = 8 cm

So, total surface area of the cube = 6 × 8 × 8
= 384 cm²

47. The area of the circle is 616 cm² and the radius of the cone is equal to the radius of the circle. If the ratio of the height and radius of the cone is 6:7, then what is the volume of the cone?

Correct Answer: (c) 2464 cm³
Solution:

22/7 × r × r = 616 cm²
Radius of the circle = 14 cm = Radius of the cone
Height of the cone = 6/7 × 14 = 12 cm

Volume of the cone = 1/3 × 22/7 × 14 × 14 × 12
= 2464 cm³

48. . Diameter of the circle is equal to the breadth of the rectangle and the ratio of the length to breadth of the rectangle is 5:4. If the perimeter of the rectangle is 126 cm, then what is the difference between the area of the circle and rectangle?

Correct Answer: (c) 364 cm²
Solution:

2 × (5x + 4x) = 126
x = 7

Breadth of rectangle = 7 × 4 = 28 cm
Diameter of the circle = 28 cm
Radius of the circle = 28/2 = 14 cm

Area of the circle = 22/7 × 14 × 14 = 616
Area of the rectangle = 35 × 28 = 980

Difference = 980 − 616 = 364 cm²

49. The curved surface of cone is 180π cm² and the radius of the cone is 12 cm. Ratio of the radius of cone to cylinder is 6:7 and the height of cylinder is 3 cm more than the height of the cone, then find the volume of the cylinder?

Correct Answer: (d) 7392 cm³
Solution:

22/7 × 12 × l = 180 × 22/7
l = 15

Height of cone = √(15² − 12²) = 9 cm
Radius of cylinder = 7/6 × 12 = 14 cm
Height of cylinder = 9 + 3 = 12 cm

Volume of cylinder = 22/7 × 14 × 14 × 12 = 392 cm³

50. If the radius of the circle is increased by 20%, then the area of the circle is increased by 271.04 cm². Find the circumference of the circle?

Correct Answer: (c) 88 cm
Solution:

Radius of the circle = x
After increased the radius = x × 120/100 = 6x/5

22/7 × 6x/5 × 6x/5 − 22/7 × x × x = 271.04
22/7 × (36x² − 25x²/25) = 271.04
11x² = 2156
x = 14

Circumference of circle = 2 × 22/7 × 14 = 88 cm