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

A cone and a cylinder have the same base radius and height. The volume of the cone is 432π cubic centimeters. What is the volume of the cylinder in cubic centimeters?

  1. 432π

  2. 864π

  3. 1,296π

  4. 1,728π
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of a cone is (1/3) * pi * r^2 * h, and the volume of a cylinder is pi * r^2 * h. Since they share the same radius and height, the cylinder volume is exactly 3 times the cone volume. 3 * 432pi = 1296pi.

Multiple choice

A chord, whose length is equal to the radius of a circle, is drawn to divide the circle into two parts. If the radius of the circle is 42 cm, then what is the area of the smaller part (in cm2)?

  1. 21 2 ( π 3 − 3 2 )

  2. 42 2 ( π 2 − 3 4 )

  3. 42 2 ( π 6 − 3 4 )

  4. 21 2 ( π 6 − 3 4 )
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A chord equal to the radius forms an equilateral triangle with the center. The area of the sector is (60/360) * pi * r^2 = (1/6) * pi * r^2. The area of the triangle is (sqrt(3)/4) * r^2. The area of the smaller segment is (pi/6 - sqrt(3)/4) * r^2. With r = 42, area = 42^2 * (pi/6 - sqrt(3)/4).

Multiple choice

The sides of a rectangle with dimension 7 cm x 11 cm are joined to form a cylinder with height 11 cm. What is the volume of this cylinder?

  1. 85.75 cm3

  2. 86.92 cm3

  3. 54.25 cm3

  4. 42.875 cm3
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When a rectangle of 7x11 is joined to form a cylinder with height 11, the circumference is 7. So 2 * pi * r = 7, which means r = 7 / (2 * pi). Volume = pi * r^2 * h = pi * (7 / (2 * pi))^2 * 11 = pi * (49 / (4 * pi^2)) * 11 = (49 * 11) / (4 * pi) = 539 / (4 * 3.14159) = 42.875.

Multiple choice

A manufacturer makes two solid cylindrical metal rods for a machine part. Each rod has a height of 36 centimeters. Rod A has a diameter of 10 centimeters, and Rod B has a diameter that is 40% greater than the diameter of Rod A. What is the volume, in cubic centimeters, of Rod B?

  1. 882π

  2. 1,296π

  3. 1,764π

  4. 7,056π
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Rod A: r = 5, h = 36. Volume A = pi * 5^2 * 36 = 900pi. Rod B: diameter is 40% greater, so diameter = 10 * 1.4 = 14. Radius = 7. Volume B = pi * 7^2 * 36 = 49 * 36 * pi = 1764pi.

Multiple choice

Directions: Each of the questions below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer: Find the height of the cylinder. I. The Curved surface area of the cylinder is 396 cm2 and the total surface area of the cylinder is 1628 cm2.II. The radius of the cylinder is 0.5 cm more than the 3 times of the height of the cylinder.

  1. The data in statements I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question.

  2. The data in statements II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question.

  3. The data in statements I alone or in statement II alone is sufficient to answer the question.

  4. The data in both the statements I and II is not sufficient to answer the question.

  5. The data in both the statements I and II together is necessary to answer the question.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Curved Surface Area (CSA) = 2*pi*r*h = 396. Total Surface Area (TSA) = 2*pi*r*h + 2*pi*r^2 = 1628. TSA - CSA = 2*pi*r^2 = 1628 - 396 = 1232. From this, r can be found, and subsequently h. Statement I is sufficient. Statement II provides a relation between r and h, but without another independent equation, it is not sufficient.

Multiple choice

Each question below contains a statement followed by Quantity I and Quantity II. Find both to find the relationship among them. Mark your answer accordingly. Quantity I: The area of the circle is 154 cm. The ratio of the radius of the Sphere and circle is 3:1. Find surface area of the sphere? Quantity II: The side of the square is equal to the breadth of the rectangle. The ratio of the length and breadth of the rectangle is 3 : 2. If the perimeter of the rectangle 70 cm, then find the sum of the area of the square and the area of the rectangle?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot beestablished
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Interpreting the circle's area as 154 cm^2 gives radius 7 cm, so the sphere radius is 21 cm and its surface area is 1764pi cm^2. For the rectangle, length and breadth are 21 cm and 14 cm, so the square plus rectangle area is 196 + 294 = 490 cm^2. Therefore, Quantity I is greater than Quantity II.

Multiple choice

Each of the questions given below consists of a statement and /or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is/are sufficient to answer the given question. A cylindrical vessel contains 80% of water in it which is filled by a pipe. Find the total capacity of the cylindrical vessel. [Use π = 3] I. The difference between the curved surface area and the total surface area of the cylindrical vessel is 384 m2. II. The pipe took 72 minutes to fill the given quantity of water at the rate of 32 m3 per minute. III. The curved surface area and total surface area of the vessel is 720 m2 and 1104 m2 , respectively. IV. The cost of painting the curved surface area of the vessel at the rate of Rs. 5 per m2 is Rs. 3600.

  1. The data either in statement I alone or in statement IV alone are sufficient to answer the question

  2. The data either in statement I alone or in statement III alone are sufficient to answer the question.

  3. The data either in statement III alone or in statement IV alone are sufficient to answer the question.

  4. The data either in statement II alone or in statement III alone are sufficient to answer the question

  5. The data in any of the four statements I, II, III or IV alone are sufficient to answer the question.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the capacity of a cylinder, we need its radius and height. Statement II provides the volume of water (32 * 72 = 2304 m^3) and the percentage filled (80%), allowing us to find the total capacity. Statement III provides the curved surface area and total surface area, which are sufficient to solve for radius and height, and thus the volume.