BANK & INSURANCE (MENSURATION) PART 1

Total Questions: 60

1. The curved surface area of a cylindrical object is 990 m² and its volume is 4455 m³. Then what is the ratio of the height and diameter of this object?

Correct Answer: (a) 35:36
Solution:

1. (a): Curved surface area = 2πrh = 990
Volume = πr²h = 4455
πrh = 495
So r = 4455/495 = 9
h = 990×7/22 × 1/9 × ½ = 35/2
So required ratio = 35:36

2. The ratio between the perimeter and the breadth of a rectangle is 15:5. If the area of the rectangle is 280 sq. cm, what is the length of the rectangle?

Correct Answer: (d) 12 cm
Solution:Let the length and breadth of the rectangle be l and b.
Therefore, (2(l + b))/b = 15/5 and l × b = 288, solving we get l = 12 and b = 24.

3. A square of area 100 m² is formed from a wire of certain length. If a rectangle is formed from the same wire, what will be its length, if length is 50% more than the width?

Correct Answer: (b) 12m
Solution:Side of square = 10 m
Perimeter of the square = 40 m
Perimeter of rectangle = 40 m
2(l + b) = 40 m
l + b = 20
l = 150% × b
3/2 b + b = 20 m
2.5b = 20, b = 8 and l = 12 m

4. A playing ground is in the form of a square one of whose side is 100 m. The area of the ground, excluding the circular area in the centre of the park is 4456 m². The radius of the circular area is-

Correct Answer: (b) 42 m
Solution:

The area of the circular area = (10000 − 4456) m² = 5544 m²
According to the question, 22/7 × r² = 5544
r² = (5544 × 7)/22 = 1764
r = √1764 = 42 m

5. The breadth of a rectangular area is 30% of its length. If the perimeter of the field is 5200 cm, find out the area of the field?

Correct Answer: (b) 120 m²
Solution:Let length = x cm.
Breadth = 0.3x cm.
Perimeter = 2(l + b) = 2(x + 0.3x) = 5200 cm
Length = x = 2000 cm, breadth = 0.3x = 600 cm
Area = 2000 × 600 / 10000 = 120 m².

6. The circumference of a circle exceeds its diameter by 30 cm. Find the circumference of the circle?

Correct Answer: (a) 44 cm
Solution:2πr − 2r = 30
2r(π − 1) = 30
2r(15/7) = 30
r = 7
Circumference = 2πr = 44 cm

7. The radius of an iron cone is 10 cm and height is 3 cm. The cone is melted and drawn into a long wire of uniform circular cross section. If the length of the wire is 25 cm, then the radius of wire is?

Correct Answer: (c) 2 cm
Solution:The volume will remain constant
Volume of wire = πr²h
1/3 × π × 10 × 10 × 3 = πr² × 25
r² = 100 × 3 / 3 × 25
r² = 4
r = 2 cm

8. The cost of fencing a circular plot at the rate of Rs. 10 per meter is Rs. 9240. What will be the cost of flooring the plot at Rs. 20 per square meter?

Correct Answer: (e) None of these
Solution:Cost of fencing the plot @ Rs. 14 per meter = Rs. 9240.
Circumference of the plot = 9240/10 = 924 m. 2πr = 924, so radius = 147 m.
Area of circular plot = π147² = 67914. So cost of flooring the plot at Rs. 20 per square meter = 67914 × 20 = Rs. 1358280.

9. A rectangle has thrice the area of a square. The length of the rectangle is 12 cm greater than the side of the square and the breadth is equal to the side of the square. Find the perimeter of the square.

Correct Answer: (e) 24 cm
Solution:

Let side of square be a. Area of square = a².
Hence area of rectangle = a × (a + 12). So, (a + 12)a = 3(a²)
which implies that a² + 12a = 3(a²); a = 6.
Hence perimeter of square = 4a = 24.

10. A circular road runs around a circular garden. If the difference between the circumference of the outer circle and inner circle is 132 m. Find the width of the road?

Correct Answer: (b) 21 m
Solution:Let R and r be the radii of the outer circle and inner circle respectively
Width of the road = R − r
2πR − 2πr = 132
2π(R − r) = 132
(R − r) = 21 m