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 right circular cone of maximum size, was carved out from a right circular cylinder (keeping the height and the radius as same as of the cylinder). The difference between the volumes of the cylinder and the conical structure was 4928 cm3. The respective ratio between the height and radius is 6 : 7. What is the height of the cylinder?

  1. 6cm

  2. 18cm

  3. 12cm

  4. 25cm

  5. 34cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = pi * r^2 * h. Volume of cone = (1/3) * pi * r^2 * h. Difference = (2/3) * pi * r^2 * h = 4928. Given h/r = 6/7, let h=6k, r=7k. (2/3) * (22/7) * (49k^2) * (6k) = 4928. 44 * 7 * 2 * k^3 = 4928. 616 * k^3 = 4928. k^3 = 8, so k = 2. Height = 6 * 2 = 12.

Multiple choice

Find the percentage increase in the total surface area when five cylinders of equal height are made from a solid cylinder of radius 3 cm and height 5 cm by cutting along the four planes parallel to the base.

  1. 134%

  2. 150%

  3. 240%

  4. 643%

  5. 86%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The original surface area is 2*pi*r^2 + 2*pi*r*h = 2*pi*9 + 2*pi*3*5 = 18*pi + 30*pi = 48*pi. Cutting the cylinder into 5 pieces creates 4 new cuts, each adding 2 circular faces of area pi*r^2 = 9*pi. Total added area is 8 * 9*pi = 72*pi. Percentage increase = (72*pi / 48*pi) * 100 = 1.5 * 100 = 150%.

Multiple choice

A girl wants to construct a circular swimming pool in her house which is in the shape of a trapezium. The lengths of the oblique sides of the house plot (in trapezium shape) are 26 m and 30 m. If the radius of the biggest circle that can be marked for the swimming pool is 12 m, then what must be the minimum area (in sq.m) of the plot?

  1. 336

  2. 672

  3. 728

  4. 1344

  5. 934
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The radius of the inscribed circle in a trapezium is related to the height. If the radius is 12, the height h = 24. For a tangential trapezium, the sum of opposite sides is equal. Sum of parallel sides = Sum of oblique sides = 26 + 30 = 56. Area = 0.5 * (sum of parallel sides) * height = 0.5 * 56 * 24 = 672.

Multiple choice

If the perimeter of a square is equal to the radius of a circle whose area is 2464 sq cm. what is the area of the square ?

  1. 49 sq cm

  2. 64 sq cm

  3. 25 sq cm

  4. 196 sq cm

  5. 81 sq cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

First, find the radius of the circle using the area formula, pi * r^2 = 2464, which gives r = 28 cm. Since the perimeter of the square is equal to this radius, we have 4 * side = 28, meaning the side of the square is 7 cm. Finally, the area of the square is side^2, which equals 49 sq cm.

Multiple choice

If the curved surface area of a solid cylinder is one-third of its total surface area, then what is the ratio of its diameter to its height?

  1. 5 : 2

  2. 1 : 1

  3. 2 : 1

  4. 4 : 1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Curved surface area (CSA) = 2*pi*r*h. Total surface area (TSA) = 2*pi*r*h + 2*pi*r^2. Given CSA = 1/3 TSA, then 3*CSA = TSA, so 6*pi*r*h = 2*pi*r*h + 2*pi*r^2. This simplifies to 4*pi*r*h = 2*pi*r^2, so 2h = r. Diameter d = 2r = 4h. Thus, d/h = 4/1.

Multiple choice

Curved surface area of a cone whose radius is 21 cm is 1914 cm2. If height of cone is half than that of perimeter of a square, then find the area of square?

  1. 36 cm2

  2. 196 cm2

  3. 100 cm2

  4. 64 cm2

  5. 144 cm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The curved surface area of a cone is pi*r*l = 1914. With r=21, l = 1914 / (22/7 * 21) = 29. Using the Pythagorean theorem, the height h = sqrt(l^2 - r^2) = sqrt(29^2 - 21^2) = sqrt(841 - 441) = 20. Since the height is half the perimeter of the square, the perimeter is 40, meaning each side is 10. The area of the square is 10^2 = 100.