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

Water is poured from a full right circular cylinder of height 3 ft and radius 2 ft into a rectangular tank whose base dimensions are 7 ft by 1 ft. Approximately, to what height, in feet, will the water rise (assume no overflow)?

  1. 5.49

  2. 5.39

  3. 5.34

  4. 5.29

  5. 5.24
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = 3.14159 * 2^2 * 3 = 37.699 ft^3. The tank base area = 7 * 1 = 7 ft^2. Height of water in tank = Volume / Base Area = 37.699 / 7 = 5.385... ft. Approximately 5.39 ft.

Multiple choice

The volume of a largest sphere that can be cut from cylindrical log of wood of base radius $1 m$ and height $4 m$ is:
  1. $\dfrac{8}{3} \pi\  m^{3}$
  2. $\dfrac{10}{3} \pi\  m^{3}$
  3. $\dfrac{16}{3} \pi\  m^{3}$
  4. $\dfrac{4}{3} \pi\  m^{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The largest sphere that can be cut from a cylinder is limited by the smaller of the base diameter or the height. Here, the base radius is 1m (diameter 2m) and height is 4m. The sphere's diameter must be 2m, so radius r = 1m. Volume = 4/3 * pi * r^3 = 4/3 * pi * 1^3 = 4/3 pi.

Multiple choice

A right circular cone has a base radius of $r$ and a height of $h.$ If the radius decrease by $20$ percent and the height increase by $10$ percent, which of the following is the resulting percent change in the volume of the cone?
  1. $10$% decrease
  2. $12$% decrease
  3. $18.4$% decrease
  4. $29.6$% decrease
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume V = (1/3) * pi * r^2 * h. New volume V' = (1/3) * pi * (0.8r)^2 * (1.1h) = (1/3) * pi * 0.64r^2 * 1.1h = 0.704 * V. This is a 29.6% decrease.

Multiple choice

A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are translated into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, then how much beverage is contained in the vessel from the bowl?
  1. $66 \frac {2}{3}$%
  2. $78 \frac {1}{2}$%

  3. 100%

  4. More than 100 % (i.e., some liquid will be the left in the bowl)
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Bowl volume = (2/3)pi*r^3. Cylinder: radius R = 1.5H. Diameter is same, so 2R = 2r, so R = r. Thus H = r/1.5 = 2r/3. Cylinder volume = pi*R^2*H = pi*r^2*(2r/3) = (2/3)pi*r^3. The volumes are equal, so 100% of the beverage fits.

Multiple choice

Length of the floor of a rectangular auditorium is $6$m more than the radius of a circle with a circumference of $572$m. The perimeter of the floor of the rectangular auditorium is $356$m. What will be the cost of flooring the auditorium(only the floor of the auditorium), if the cost of flooring is Rs. $12/m^2?$
  1. Rs. $87,954$
  2. Rs. $91,236$
  3. Rs. $94,284$
  4. Rs. $75,490$

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

Circumference = 2 * pi * r = 572, so r = 572 / (2 * 22/7) = 91m. Length = 91 + 6 = 97m. Perimeter = 2(L + B) = 356, so 97 + B = 178, B = 81m. Area = 97 * 81 = 7857 m^2. Cost = 7857 * 12 = 94284.