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

One boy has two toys of equal areas; one is in the shape of a right-anglde triangle whose base and height are the same and the other one is in the shape of a rectangle whose area is 200 cm2. Find the height of the triangular-shaped toy.

  1. 20 cm

  2. 10 cm

  3. 40 cm

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Triangle area = (1/2) * base * height. Since base = height = h, Area = 0.5 * h^2. Rectangle area = 200. 0.5 * h^2 = 200, so h^2 = 400, h = 20.

Multiple choice

A milkman uses a cylindrical container of height 25 cm and curved surface area 1100 cm2. Find the total surface area of the container used by the milkman.

  1. 1100 cm2

  2. 1408 cm2

  3. 708 cm2

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

CSA = 2*pi*r*h = 1100. 2*pi*r*25 = 1100, so 2*pi*r = 44. TSA = CSA + 2*pi*r^2 = 1100 + r*(2*pi*r) = 1100 + r*44. Since 2*pi*r = 44, r = 44/(2*pi) = 22/pi. TSA = 1100 + (22/pi)44 = 1100 + 968/pi. Using pi = 22/7, TSA = 1100 + 968(7/22) = 1100 + 308 = 1408.

Multiple choice

Directions: Solve the following question and mark the best possible option. A solid metallic cube is melted to form five solid cubes whose volumes are in the ratio 1 : 1 : 8 : 27 : 27. The percentage by which the sum of the surface areas of these five cubes exceeds the surface area of the original cube is nearest to

  1. 10

  2. 50

  3. 60

  4. 20
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let the original volume be V. The five cubes have volumes V/40, V/40, 8V/40, 27V/40, 27V/40 (summing to V). Calculating the surface areas (proportional to volume^(2/3)) and comparing the sum to the original cube's surface area shows an increase of approximately 50%.

Multiple choice

What would be the area of square whose area is equal to the area of circle of diameter 28 cm?

  1. 298 cm2

  2. 616 cm2

  3. 780 cm2

  4. 808 cm2

  5. 858 cm2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The radius of the circle is half of its diameter, which is 14 cm. The area of the circle is calculated as pi * r^2, which equals (22/7) * 14 * 14 = 616 square centimeters. Since the area of the square is equal to the area of the circle, the area of the square is also 616 square centimeters.

Multiple choice

A right angle is enclosed by the sides of a triangle measuring 3.5 cm and 45 cm. The triangle is rotated about one of its longer perpendicular sides. Find the volume of the solid, thus traced.

  1. 144.3 cm3

  2. 454.3 cm3

  3. 577.5 cm3

  4. 664.6 cm3

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

Rotating the right-angled triangle about its longer perpendicular side (45 cm) forms a cone with a height of 45 cm and a base radius of 3.5 cm. The volume of this cone is (1/3) * pi * r^2 * h = (1/3) * (22/7) * 3.5 * 3.5 * 45, which simplifies to 577.5 cubic centimeters.