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

In the science class, two students, Alex and Bella, are working on a project involving the study of spherical objects. Alex has a smaller hemispherical bowl (H1), and Bella has a larger hemispherical bowl (H2). If the ratio of the volumes of H1 to H2 is 8 : 27, what is the ratio of the curved surface areas of H1 to H2?

  1. 4 : 9

  2. 16 : 81

  3. 8 : 27

  4. 64 : 729

  5. 2 : 3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The volume of a sphere is proportional to the cube of its radius (V proportional to r^3), so the ratio of radii is the cube root of the volume ratio. The cube root of 8:27 is 2:3. Surface area is proportional to the square of the radius (A proportional to r^2), so the ratio of surface areas is (2^2):(3^2), which is 4:9.

Multiple choice

In a scientific experiment, researchers are examining a cylindrical chamber. If the radius of the chamber is increased by 20% and the height is decreased by 10%, resulting in an increase in volume of 296 cubic units, what is the original volume of the cylindrical chamber?

  1. 1,000 cubic units

  2. 1,184 cubic units

  3. 1,328 cubic units

  4. 1,472 cubic units

  5. 1,616 cubic units
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let V = pi*r^2*h. The new volume is pi*(1.2r)^2*(0.9h) = pi*1.44*r^2*0.9*h = 1.296*V. The increase is 0.296*V = 296, so V = 1,000.

Multiple choice

A cylindrical-shaped water tank has the sum of its radius and height equal to 26 units. Additionally, the curved surface area of the tank is 2,772 square units less than the total surface area. Find the total surface area of the cylindrical-shaped water tank.

  1. 660 square units

  2. 2,772 square units

  3. 3,076 square units

  4. 3,432 square units

  5. 3,626 square units
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The difference between the total surface area and the curved surface area of a cylinder is the area of its two circular bases, which is 2 * pi * r^2. Setting this equal to 2,772 gives r = 21. Since the sum of the radius and height is 26, the total surface area is 2 * pi * r * (r + h) = 2 * (22/7) * 21 * 26 = 3,432 square units.

Multiple choice

In a small town, Marcus, a famous craftsman known for his metalwork, was asked by the local community center to make a large hemispherical bowl for their annual festival. Marcus had a rectangular metal container lying around, measuring 5.5 meters long, 3 meters wide, and 1.176 meters high. He melted the metal and expertly shaped it into the desired hemispherical form. What would be the radius of that new hemispherical bowl Marcus had crafted? (Use π = 22/7)

  1. 1.4 m

  2. 2.1 m

  3. 2.8 m

  4. 3.5 m

  5. 4.0 m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of rectangular container = 5.5 * 3 * 1.176 = 19.404 cubic meters. Volume of hemisphere = (2/3) * pi * r^3. (2/3) * (22/7) * r^3 = 19.404. (44/21) * r^3 = 19.404. r^3 = 19.404 * 21 / 44 = 9.261. r = cube root of 9.261 = 2.1.

Multiple choice

For a school science project, Alice made a certain number of identical rocket prototypes comprising a cylindrical body for the fuselage, extending up to a height of 10 centimeters, and a conical nose cone representing the rocket's tip. If a total of 2,772 square centimeters of metal sheet was used in constructing all the rockets for the science project, with the base diameters of both the cylinder and the cone being 7 centimeters, and the slant height of the conical part being 8 centimeters, how many rockets did Alice make for the project?

  1. 7

  2. 8

  3. 9

  4. 10

  5. 11
Reveal answer Fill a bubble to check yourself
B Correct answer
Multiple choice

A carpenter is designing a rectangular table with an area of x square meters. However, upon reconsideration, the carpenter decides to increase the length of the table by 20%. Realizing that the table is now too large, the carpenter decides to decrease the width by 15%. What is the area of the modified table in terms of x?

  1. 0.85x

  2. 1.02x

  3. 1.2x

  4. 1.34x

  5. 1.5x
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let length be L and width be W, so x = L * W. The new length is 1.2L and the new width is 0.85W. The new area is 1.2 * 0.85 * L * W = 1.02 * L * W = 1.02x.

Multiple choice

Lisa plans to decorate the ceiling of her small cuboidal-shaped room. She knows that the total surface area of the room is 56 square meters, with a lateral surface area of 36 square meters. What is the area, in square meters, of the ceiling that she plans to decorate?

  1. 7

  2. 8

  3. 9

  4. 10

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

Total surface area = 2(lb + bh + lh) = 56. Lateral surface area = 2h(l+b) = 36. Total surface area = Lateral + 2(lb) = 56. 36 + 2(lb) = 56, so 2(lb) = 20, lb = 10. The area of the ceiling is lb = 10.

Multiple choice

In a household, a cylindrical tank is designated for water storage. The tank has a diameter of 10 feet and a height of 7 feet. The homeowner plans to paint the cylindrical tank, leaving the top and bottom surfaces unpainted. What is the total surface area, in square feet, of the cylindrical tank that needs to be painted?

  1. 14π

  2. 35π

  3. 70π

  4. 175π
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The lateral surface area of a cylinder is 2 * pi * r * h. Given diameter = 10 feet, radius r = 5 feet. Height h = 7 feet. Area = 2 * pi * 5 * 7 = 70 * pi square feet.

Multiple choice

The surface area of a cylinder is 33x2 square units. The sum of the radius and the height of the cylinder is 6x units. What is the circumference of the base of the cylinder, in units?

  1. 5.5x

  2. 8.5x

  3. 11x

  4. 12x
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The total surface area of a cylinder is given by the formula 2 * pi * r * (r + h), where r is the radius and h is the height. Substituting the given surface area of 33x^2 and the sum of the radius and height of 6x, we get 2 * pi * r * (6x) = 33x^2. Solving for the circumference, which is 2 * pi * r, yields 33x^2 / 6x = 5.5x.

Multiple choice

What is the total surface area (in square centimeters) of the cuboid formed when John, Sarah, and Michael joined their Rubik cubes face to face, each having a volume of 1,331 centimeters³?

  1. 121

  2. 968

  3. 1,694

  4. 1,936
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume = 1331, so side length = cube root of 1331 = 11 cm. Three cubes joined face to face form a cuboid of dimensions 11 x 11 x 33. Surface area = 2 * (lw + lh + wh) = 2 * (11*11 + 11*33 + 11*33) = 2 * (121 + 363 + 363) = 2 * 847 = 1694.

Multiple choice

A solid metallic cube has a side length of 14 cm. The largest possible sphere is carved out from this cube. What is the approximate volume of the material wasted (i.e., the volume of the cube remaining after the sphere is carved out)? (Use π=22/7)

  1. 4204

  2. 1306

  3. 7603

  4. 4003

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Cube volume = 14^3 = 2744. Sphere radius = 7. Sphere volume = 4/3 * 22/7 * 7^3 = 4/3 * 22 * 49 = 4312/3 = 1437.33. Wasted = 2744 - 1437.33 = 1306.67.

Multiple choice

A cylindrical water storage tank needs to be filled. The tank has a radius of 3.5 meters and a height of 10 meters. What is the maximum volume of water (in liters) that the tank can hold? (Use π=22/7 and assume 1 cubic meter = 1000 liters)

  1. 5,64,000

  2. 3,85,000

  3. 796,000

  4. 544,000

  5. 236,000
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume = pi * r^2 * h = (22/7) * (3.5)^2 * 10 = (22/7) * 12.25 * 10 = 22 * 1.75 * 10 = 385 cubic meters. 385 * 1000 = 385,000 liters.