Mensuration: Bank Exam Practice Questions (SBI, IBPS, RRB, PO & Clerk)
Q. 1 A circle with a radius of 8 cm is removed from a rectangle that is 18 cm long and 16 cm wide. What percentage of the rectangle’s remaining area is the circle’s area, rounded to the nearest whole percentage?
Check Solution
Ans: D
Explanation: 1. Calculate the area of the rectangle: Length x Width = 18 cm * 16 cm = 288 sq cm.
2. Calculate the area of the circle: π * radius^2 = π * 8^2 = 64π sq cm ≈ 201.06 sq cm.
3. Calculate the remaining area of the rectangle: 288 sq cm – 201.06 sq cm = 86.94 sq cm.
4. Calculate the percentage of the remaining area that is the circle’s area: (Circle’s Area / Remaining Area) * 100% = (201.06 / 86.94) * 100% ≈ 231.27%
5. Round to the nearest whole percentage: 231%
Q. 2 A circle’s area matches a rectangle’s area. The rectangle’s perimeter is 144 cm, and its length is 16 cm longer than its width. Find the circle’s radius.
Check Solution
Ans: E
Explanation: Let the width of the rectangle be ‘w’ cm. Then the length is ‘w + 16’ cm. The perimeter of the rectangle is given by 2(length + width) = 144 cm. So, 2(w + 16 + w) = 144, which simplifies to 2(2w + 16) = 144. Dividing by 2, we have 2w + 16 = 72. Subtracting 16, 2w = 56, and w = 28 cm. The length is therefore 28 + 16 = 44 cm. The area of the rectangle is length * width = 44 * 28 = 1232 sq cm. Since the area of the circle is equal to the area of the rectangle, the area of the circle is 1232 sq cm. The area of a circle is given by πr^2, where r is the radius. Thus, πr^2 = 1232. Assuming π = 22/7, then (22/7) * r^2 = 1232. Multiplying by 7/22, r^2 = 1232 * (7/22) = 56 * 7 = 392. Taking the square root, r = sqrt(392) = 14 * sqrt(2) which is approximately 19.8 cm. None of the given options are matching.
Correct Option: E
Q. 3 A circle’s diameter is double the length of a rectangle. If the ratio of the circle’s area to the rectangle’s area is 11:7, what’s the ratio of the rectangle’s length to its breadth?
Check Solution
Ans: A
Explanation: Let the rectangle’s length and breadth be ‘l’ and ‘b’ respectively. The diameter of the circle is 2l. The radius of the circle is l.
Area of the circle = πr² = πl²
Area of the rectangle = lb
Given: (Area of circle) / (Area of rectangle) = 11/7
πl² / lb = 11/7
Since the diameter is twice the length of the rectangle:
Diameter = 2l, therefore r = l.
πl²/lb = 11/7
Since π is approximately 22/7, we can substitute.
(22/7)l²/lb = 11/7
2l/b = 1/1
2l = b x 1
l / b = 1/2
Therefore the ratio of length to breadth is 1:2.
Correct Option: A
Q. 4 A cylinder’s height is twice its base radius. If the circular base has an area of 154 cm², calculate the cylinder’s curved surface area.
Check Solution
Ans: C
Explanation:
1. **Find the radius:** The area of the circular base is πr², so πr² = 154 cm². Using π ≈ 22/7, we have (22/7) * r² = 154. Therefore, r² = 154 * (7/22) = 49, and r = 7 cm.
2. **Find the height:** The height (h) is twice the radius, so h = 2 * 7 cm = 14 cm.
3. **Calculate the curved surface area:** The curved surface area of a cylinder is 2πrh. Substituting the values, we get 2 * (22/7) * 7 cm * 14 cm = 616 cm².
Correct Option: C
Q. 5 A cylinder’s volume is 616 cubic meters and its curved surface area is 352 square meters. What is the cylinder’s total surface area?
Check Solution
Ans: A
Explanation: Let the radius of the cylinder be r and the height be h.
Volume of cylinder = πr²h = 616 …(1)
Curved Surface Area = 2πrh = 352 …(2)
Dividing (1) by (2):
(πr²h) / (2πrh) = 616/352
r/2 = 7/4
r = (7/4) * 2 = 7/2
Substituting r in equation (2):
2 * (22/7) * (7/2) * h = 352
22h = 352
h = 16
Now we can calculate the total surface area which is 2πr(h+r):
Total Surface Area = 2πr² + 2πrh = 2 * (22/7) * (7/2)² + 352
= 2 * (22/7) * (49/4) + 352
= 77 + 352 = 429 m²
Correct Option: A
Q. 6 A hemispherical pot with a curved surface area of 882π sq cm is filled with milk. This milk is then poured into a cylindrical can that has the same radius as the hemispherical pot, completely filling the can. What is the height of the cylindrical can?
Check Solution
Ans: C
Explanation: The curved surface area of a hemisphere is 2πr². We are given that 2πr² = 882π. Dividing both sides by 2π, we get r² = 441. Therefore, the radius r = √441 = 21 cm. The volume of the hemispherical pot (volume of milk) is (2/3)πr³ = (2/3)π(21)³ = (2/3)π(9261) = 6174π cm³. The volume of a cylinder is πr²h. We know the cylindrical can has the same radius as the hemisphere, which is 21cm, and its volume is also 6174π cm³. Thus, π(21)²h = 6174π. Dividing both sides by π, we get 441h = 6174. Solving for h, we get h = 6174 / 441 = 14 cm.
Correct Option: C
Q. 7 A rectangle’s area is three times bigger than a square’s area. If the square has a side of 4 cm and this side also represents the width of the rectangle, what is the length of the rectangle?
Check Solution
Ans: C
Explanation: First, calculate the area of the square: Area = side * side = 4 cm * 4 cm = 16 sq cm.
Next, find the area of the rectangle: Area = 3 * square’s area = 3 * 16 sq cm = 48 sq cm.
The width of the rectangle is given as 4 cm.
Finally, calculate the length of the rectangle: Length = Area / Width = 48 sq cm / 4 cm = 12 cm.
Correct Option: C
Q. 8 A rectangle’s length and width are proportional, with the length being 4 parts and the width 3 parts. Knowing the rectangle’s area is 108 square meters, what’s the area of a square if its side is the same length as the rectangle’s width?
Check Solution
Ans: C
Explanation: Let the length be 4x and the width be 3x. The area of the rectangle is length * width = (4x)(3x) = 12x2. We are given the area is 108 m2, so 12x2 = 108. Dividing both sides by 12, we get x2 = 9. Taking the square root of both sides, we get x = 3. Therefore, the width of the rectangle is 3x = 3 * 3 = 9 meters. The side of the square is the same as the rectangle’s width, so the side of the square is 9 meters. The area of the square is side * side = 9 * 9 = 81 m2.
Correct Option: C
Q. 9 A rectangle’s length exceeds its width by 3 cm. The area difference between a circle and this rectangle is 84 cm², with the circle’s area being larger. Determine the rectangle’s length, given the circle’s radius is 7 cm.
Check Solution
Ans: B
Explanation:
1. **Calculate the circle’s area:** Area of a circle = πr², where r = 7 cm. Area = π * 7² = 49π ≈ 49 * (22/7) = 154 cm².
2. **Determine the rectangle’s area:** The area difference is 84 cm² (circle’s area is larger). Therefore, rectangle’s area = Circle’s area – Difference = 154 cm² – 84 cm² = 70 cm².
3. **Set up equations for the rectangle:** Let the width of the rectangle be ‘w’. The length is ‘w + 3’. Area of rectangle = length * width, so w * (w + 3) = 70.
4. **Solve the quadratic equation:** w² + 3w = 70. Rearrange to w² + 3w – 70 = 0. Factorize to (w + 10)(w – 7) = 0. Therefore w = -10 or w = 7. Since width cannot be negative, w = 7 cm.
5. **Calculate the length:** Length = w + 3 = 7 + 3 = 10 cm.
Correct Option: B
Q. 10 A rectangular field has a perimeter of 420 meters. The length is 30 meters longer than the width. If someone walks diagonally across the field at a speed of 10 meters per second, how long will it take them?
Check Solution
Ans: A
Explanation: Let the width of the field be ‘w’ meters. The length is ‘w + 30’ meters. The perimeter is 2 * (length + width) = 420 meters.
So, 2 * (w + 30 + w) = 420
2 * (2w + 30) = 420
4w + 60 = 420
4w = 360
w = 90 meters (width)
Length = w + 30 = 90 + 30 = 120 meters.
Now, we need to find the diagonal. Using the Pythagorean theorem: diagonal^2 = length^2 + width^2
diagonal^2 = 120^2 + 90^2 = 14400 + 8100 = 22500
diagonal = sqrt(22500) = 150 meters.
The person walks at 10 meters per second.
Time = Distance / Speed = 150 meters / 10 m/s = 15 seconds.
Correct Option: A
Q. 11 A rectangular field is 54 meters long and 26 meters wide. A 4-meter wide path runs across the middle of the field, parallel to the shorter side. Calculate the area of the field that isn’t the path.
Check Solution
Ans: D
Explanation: The path runs parallel to the shorter side, so it has the same width as the field.
The total area of the field = length * width = 54 meters * 26 meters = 1404 sq.m.
Area of path = length of path * width of path = 26 * 4 = 104 sq. meters
Area of the remaining field = (total area) – Area of path = (54 * 26) – (26 * 4) = 1404 – 104 = 1300 sq. meters
Correct Option: D
Q. 12 A sphere has a total surface area of 400π square meters. A rectangle’s length matches the sphere’s diameter. If the rectangle’s width is 3 meters less than its length, what is the rectangle’s area?
Check Solution
Ans: E
Explanation: First, find the sphere’s radius. The surface area of a sphere is 4πr², where r is the radius. We’re given 400π = 4πr². Divide both sides by 4π to get 100 = r². Therefore, r = 10 meters. The diameter is twice the radius, so the diameter is 2 * 10 = 20 meters. The rectangle’s length is equal to the sphere’s diameter, so the length is 20 meters. The width is 3 meters less than the length, so the width is 20 – 3 = 17 meters. The area of the rectangle is length times width, so the area is 20 * 17 = 340 square meters.
Correct Option: E
Q. 13 A square and a rectangle have the same area. The rectangle’s length is 8 cm longer than the side of the square, and its width is 6 cm shorter than the square’s side. What is the perimeter of the rectangle?
Check Solution
Ans: C
Explanation: Let ‘s’ be the side of the square. Then the area of the square is s². The length of the rectangle is s + 8, and the width is s – 6. The area of the rectangle is (s + 8)(s – 6). Since the areas are equal, we have s² = (s + 8)(s – 6). Expanding the right side gives s² = s² + 2s – 48. Subtracting s² from both sides gives 0 = 2s – 48. So, 2s = 48, and s = 24 cm. The length of the rectangle is 24 + 8 = 32 cm, and the width is 24 – 6 = 18 cm. The perimeter of the rectangle is 2(length + width) = 2(32 + 18) = 2(50) = 100 cm.
Correct Option: C
Q. 14 The dimensions of a rectangular floor are 25 meters by 18 meters. If the total cost of tiling the floor is Rs. 9000, what is the cost per square meter?
Check Solution
Ans: B
Explanation: First, calculate the area of the rectangular floor: Area = length * width = 25 meters * 18 meters = 450 square meters. Next, calculate the cost per square meter by dividing the total cost by the area: Cost per square meter = Total cost / Area = Rs. 9000 / 450 square meters = Rs. 20 per square meter.
Q. 15 The length and breadth of a rectangle are in the ratio of 4:5. If the area of the rectangle is 180 cm², find its perimeter.
Check Solution
Ans: C
Explanation: Let the length and breadth of the rectangle be 4x and 5x respectively. The area of the rectangle is given by length * breadth, which is (4x)(5x) = 20x². We are given that the area is 180 cm². So, 20x² = 180. Dividing both sides by 20, we get x² = 9. Taking the square root of both sides, we get x = 3. Therefore, the length is 4 * 3 = 12 cm, and the breadth is 5 * 3 = 15 cm. The perimeter of a rectangle is 2 * (length + breadth). So, the perimeter is 2 * (12 + 15) = 2 * 27 = 54 cm.
Q. 16 Two cylinders have the same radius of 2 meters. Their curved surface areas are 88 m² and 132 m². What is the ratio of their heights?
Check Solution
Ans: D
Explanation: The curved surface area of a cylinder is given by 2πrh, where r is the radius and h is the height. Let h1 and h2 be the heights of the two cylinders. We are given that the radius (r) is the same for both cylinders, and r = 2 meters. Let CSA1 and CSA2 be the curved surface areas of the two cylinders.
CSA1 = 2πrh1 = 88 m²
CSA2 = 2πrh2 = 132 m²
We want to find the ratio h1 : h2. Dividing the first equation by the second equation:
(2πrh1) / (2πrh2) = 88 / 132
h1 / h2 = 88 / 132
h1 / h2 = (2*44) / (3*44)
h1 / h2 = 2 / 3
Therefore the ratio of their heights is 2:3.
Next Chapter: Mixtures and Alligations
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