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 solid consists of a circular cylinder fitted with right circular cone placed on the top. The height of the cone is 9 cm. If total volume of the solid is 3 times the volume of the cone, find the height of the circular cylinder.

  1. 6 cm

  2. 7 cm

  3. 8 cm

  4. 7.5 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * 9 = 3 * pi * r^2. Volume of solid = Volume of cylinder + Volume of cone = pi * r^2 * H + 3 * pi * r^2. Given Volume of solid = 3 * Volume of cone = 3 * (3 * pi * r^2) = 9 * pi * r^2. So, pi * r^2 * H + 3 * pi * r^2 = 9 * pi * r^2. H + 3 = 9, so H = 6 cm.

Multiple choice

A metallic right circular cone of height 36 cm and base radius 7 cm is melted and recast into a cuboid whose length and breadth are 22 cm and 6 cm, respectively. What is the height of the cuboid?

  1. 10 cm

  2. 12 cm

  3. 14 cm

  4. 16 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The volume of the cone is (1/3) * pi * r^2 * h = (1/3) * (22/7) * 7 * 7 * 36 = 1848 cm^3. Equating this to the volume of the cuboid (l * b * h = 22 * 6 * h), we get 132 * h = 1848, so h = 14 cm.

Multiple choice

If the height of a cylinder becomes 1/4 of the original height and the radius is doubled. Then which of the following will be true?

  1. Volume of the cylinder will be doubled.

  2. Volume of the cylinder will remain unchanged.

  3. Volume of cylinder will be halved

  4. Volume of the cylinder will be 1/4
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of a cylinder is V = pi * r^2 * h. New volume V' = pi * (2r)^2 * (h/4) = pi * 4r^2 * h/4 = pi * r^2 * h. The volume remains unchanged.

Multiple choice

A circle of radius 6 cm is placed overlapping a square of area 128 cm2, such that the centre of the circle lies at the point of intersection of the diagonals of the square. What is the maximum distance between any vertex of the square and any point on the circumference of the circle?

  1. 10 cm

  2. 12 cm

  3. 14 cm

  4. 16 cm

  5. 18 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Area of square = 128, so side length s = sqrt(128) = 8 * sqrt(2). Distance from center to vertex = (1/2) * diagonal = (1/2) * (s * sqrt(2)) = (1/2) * (8 * sqrt(2) * sqrt(2)) = 8 cm. The circle has radius 6 cm. The maximum distance from a vertex to any point on the circle is the distance from the vertex to the center plus the radius: 8 + 6 = 14 cm.

Multiple choice

A sphere of 80 cm diameter is dropped into a cylindrical vessel of 40 cm radius, partially filled with water. The level of water rises by 'a'. What is the value of 'a'?

  1. 53.33 cm

  2. 50.33 cm

  3. 40 cm

  4. 20 cm

  5. 80 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of sphere = (4/3) * pi * r^3 = (4/3) * pi * 40^3 = 85333.33 * pi. Volume of water rise in cylinder = pi * R^2 * a = pi * 40^2 * a = 1600 * pi * a. Equating them: 1600 * a = 85333.33, so a = 53.33 cm.

Multiple choice

The volume of a right circular cylinder is the same numerical value as its total surface area. Find the smallest integral value for the radius of the cylinder.

  1. 1

  2. 2

  3. 3

  4. 4

  5. This value cannot be determined.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cylinder = pi * r^2 * h. Total surface area = 2 * pi * r * h + 2 * pi * r^2. Setting them equal: pi * r^2 * h = 2 * pi * r * (h + r). r * h = 2 * (h + r). r * h = 2h + 2r. h(r - 2) = 2r. h = 2r / (r - 2). For h > 0, r must be > 2. The smallest integer r > 2 is 3.

Multiple choice

A right circular cone whose base radius is 4 is inscribed in a sphere of radius 5. What is the ratio of the volume of the cone to the volume of the sphere?

  1. 0.222 : 1

  2. 0.256 : 1

  3. 0.288 : 1

  4. 0.333 : 1

  5. 0.864 : 1
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a cone of radius r=4 in a sphere of radius R=5, the height h is found via Pythagoras: (h-R)^2 + r^2 = R^2, so (h-5)^2 + 16 = 25, h-5 = 3, h=8. Volume of cone = (1/3)pi(r^2)h = (1/3)pi(16)(8) = 128pi/3. Volume of sphere = (4/3)pi(R^3) = (4/3)pi(125) = 500pi/3. Ratio = (128/3) / (500/3) = 128/500 = 0.256.