Quantitative Aptitude

Mensuration

2,507 Questions
All Direct Formula Application 1067 Shape Transformations 343 Mensuration Ratio Equations 277 Combined & Hollow Solids 247 Successive Percentage Changes 178 Inscribed & Circumscribed Figures 165 Cost Estimation Problems 100 Liquid Pour & Submergence 67 Unit Conversions 35 Path & Border Calculations 17 Time & Work Integration 7 Scale & Model Proportions 2

Mensuration Questions

Multiple choice

If diameter of the circular park is equal to the perimeter of the square whose area is 1764 m².The what will be the cost of fencing in rs the circular park at rate of rs. 60 per meter ?

  1. 34000

  2. 31680

  3. 36500

  4. 34620

  5. Can not be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The square has side sqrt(1764) = 42 m, so its perimeter is 168 m. This is the circular park's diameter, giving circumference = 22/7 x 168 = 528 m. The fencing cost is 528 x 60 = Rs. 31,680.

Multiple choice

A solid metallic cylinder of height 8 cm and radius 7 cm is melted and recast into a cone of height 24 cm. By what % is the lateral surface area of cone more than that of the cylinder ?

  1. 33.3%

  2. 37.5%

  3. 44.4%

  4. 56.2%

  5. 48.8%
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Cylinder: V = pi*7^2*8 = 392*pi. Cone: V = 1/3*pi*r^2*24 = 8*pi*r^2. 8*r^2 = 392, r^2 = 49, r = 7. Slant height l = sqrt(7^2 + 24^2) = 25. Lateral Area of Cone = pi*r*l = pi*7*25 = 175*pi. Lateral Area of Cylinder = 2*pi*r*h = 2*pi*7*8 = 112*pi. Increase = (175-112)/112 = 63/112 = 0.5625 = 56.25%.

Multiple choice

A rectangular solid has length 10 cm, width 6 cm, and height 4 cm. The length is increased by 20%, the width is decreased by 25%, and the height remains the same. Quantity A The volume of the new solid Quantity B 261 cubic centimeters

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Original volume = 10 * 6 * 4 = 240. New length = 12, new width = 4.5, height = 4. New volume = 12 * 4.5 * 4 = 216. Since 216 < 261, Quantity B is greater.

Multiple choice

A solid plastic sphere with a radius of 6 cm is melted and recast into a right circular cylindrical rod with a radius of 3 cm. What is the ratio of the total surface area of the cylindrical rod to that of the original sphere?

  1. 24 : 35

  2. 35 : 24

  3. 5 : 3

  4. 7 : 4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of sphere = (4/3) * pi * 6^3 = 288 * pi. Volume of cylinder = pi * 3^2 * h = 9 * pi * h. Equating volumes, 9 * pi * h = 288 * pi, so h = 32. Surface area of sphere = 4 * pi * 6^2 = 144 * pi. Surface area of cylinder = 2 * pi * 3^2 + 2 * pi * 3 * 32 = 18 * pi + 192 * pi = 210 * pi. The ratio is 210 : 144, which simplifies to 35 : 24.

Multiple choice

What is the total cost of painting the four walls of arectangular room?Statement I: The total area of the four walls is 120 squaremetres.Statement II: The height of the room is 5 metres.Statement III: The cost of painting is 25 per square metre.

  1. a.Only I and II are sufficient.

  2. b. Only II and III are sufficient.

  3. c. Only I and III are sufficient.

  4. d. All I, II, and III are sufficient.

  5. e. Neither I, II, and III are sufficient.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the total cost, you need the total area (Statement I) and the cost per square metre (Statement III). The height (Statement II) is redundant because the total area is already provided.

Multiple choice

The length of a rectangular conference hall is 6 meters more than its breadth. If the total cost of flooring the hall at a commercial rate of Rs. 85 per square meter is Rs. 18,360, evaluate the perimeter of the conference hall.

  1. 54 meters

  2. 60 meters

  3. 64 meters

  4. 72 meters

  5. 58 meters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area = 18360 / 85 = 216 sq meters. Let breadth be x, length x+6. x(x+6) = 216. x^2 + 6x - 216 = 0. (x+18)(x-12) = 0. Breadth = 12, Length = 18. Perimeter = 2 * (12 + 18) = 60 meters.

Multiple choice

A gift box in the shape of a right prism with a square base has a height of 20 centimetres. The total surface area of the gift box is 1,000 square centimetres. What will be the volume of the gift box in cubic centimetres?

  1. 1,500

  2. 1,600

  3. 1,800

  4. 2,000
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let the side of the square base be s. The surface area is 2s^2 + 4sh = 1000. Given h = 20, we have 2s^2 + 80s - 1000 = 0, which simplifies to s^2 + 40s - 500 = 0. Solving for s gives (s+50)(s-10) = 0, so s = 10. The volume is s^2 * h = 10^2 * 20 = 2000.