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

The plinth of a house has an area of 200 square metres. It is rectangular in shape and its length and breadth are in the ratio 2 : 1. The owner of the house extends the terrace by 1 m on each side. What is the percentage of area that has increased in the terrace relative to the plinth?

  1. 40%

  2. 32%

  3. 20%

  4. 15.5%
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area = 200, ratio 2:1. 2x * x = 200 => x^2 = 100 => x = 10. Dimensions are 20m and 10m. New dimensions after 1m extension on each side: (20+2) and (10+2) = 22m and 12m. New area = 22 * 12 = 264. Increase = 64. Percentage increase = (64/200) * 100 = 32%.

Multiple choice

A conical tent has a height of 12 metres and a floor area of 616 square metres. If the canvas used for the tent is 1.2 metres wide, what is the approximate length of canvas required to build the tent?

  1. 576.13 m

  2. 676.13 m

  3. 746.36 m

  4. 846.43 m

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

Area = pi * r^2 = 616. r^2 = 616 * 7 / 22 = 196, so r = 14. Slant height l = sqrt(r^2 + h^2) = sqrt(14^2 + 12^2) = sqrt(196 + 144) = sqrt(340) approx 18.44. Lateral surface area = pi * r * l = (22/7) * 14 * 18.44 = 44 * 18.44 = 811.36. Length of canvas = Area / width = 811.36 / 1.2 = 676.13.

Multiple choice

A hemispherical bowl of internal radius 18 cm is full of liquid. This liquid is to be filled in cylindrical bottles each of radius 3 cm and height 6 cm. How many bottles are required to empty the bowl?

  1. 72

  2. 70

  3. 68

  4. 66
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of the hemispherical bowl = (2/3) * pi * r^3 = (2/3) * pi * 18^3 = 3888 * pi. Volume of one cylindrical bottle = pi * r^2 * h = pi * 3^2 * 6 = 54 * pi. Number of bottles = (3888 * pi) / (54 * pi) = 72.

Multiple choice

The ratio between the height and radius of the base of a cylinder is 7 : 5. If its volume is 14836.5 cm3, then find its total surface area (take π = 3.14).

  1. 3391.2 cm2

  2. 5391.2 cm2

  3. 4391.2 cm2

  4. 5591.2 cm2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given h/r = 7/5, let h = 7x and r = 5x. Volume V = pi * r^2 * h = 3.14 * (5x)^2 * (7x) = 3.14 * 25 * 7 * x^3 = 549.5 * x^3. Setting 549.5 * x^3 = 14836.5 gives x^3 = 27, so x = 3. Thus, r = 15 and h = 21. Total surface area = 2 * pi * r * (r + h) = 2 * 3.14 * 15 * (15 + 21) = 94.2 * 36 = 3391.2.

Multiple choice

The radius of a cylinder is increased by 120% and its height is decreased by 40%. What is the percentage increase in its volume?

  1. 180.6%

  2. 212.8%

  3. 190.4%

  4. 175.4%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of a cylinder is V = pi * r^2 * h. If radius increases by 120%, the new radius is 2.2r. If height decreases by 40%, the new height is 0.6h. The new volume is pi * (2.2r)^2 * (0.6h) = pi * 4.84r^2 * 0.6h = 2.904 * V. This represents a 190.4% increase.

Multiple choice

The height of a right circular cylinder is 12.6 cm. Find the volume of the cylinder, if three times the sum of areas of its two circular faces is twice the area of its curved surface.

  1. 11,177 cu. cm

  2. 2,794 cu. cm

  3. 698 cu. cm

  4. 14,145 cu. cm

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

Given height h = 12.6, the condition is 3 * (2 * pi * r^2) = 2 * (2 * pi * r * h). Simplifying, 6 * pi * r^2 = 4 * pi * r * h, which leads to 3r = 2h. Thus, r = (2 * 12.6) / 3 = 8.4. The volume is pi * r^2 * h = pi * (8.4)^2 * 12.6, which is approximately 2794.

Multiple choice

In a town's central park, a beautiful fountain is constructed in the shape of a circular basin, which is inscribed in a square platform. Within this circular basin, a skilled artist creates a captivating artwork of a triangular shape with sides 5 m, 12 m and 13 m such that all three endpoints of the triangular artwork touch the boundary of the circular basin. What is the area of the square platform?

  1. 42.25 m2

  2. 100 m2

  3. 156.25 m2

  4. 169 m2

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

A triangle with sides 5, 12, 13 is a right-angled triangle. The circumradius of a right triangle is half the hypotenuse, so the radius of the circle is 13/2 = 6.5 m. The circle is inscribed in a square, so the side of the square is equal to the diameter of the circle, which is 13 m. Area of the square = 13*13 = 169 m^2.

Multiple choice

A city designs a water storage system. This system features a unique water tank in the form of a right circular cylinder. The cylinder is carefully crafted to fit inside a spherical container with a radius of 6 metres. The height of the cylinder is 10 metres. What is the amount of water that this specific cylindrical tank is capable of holding? (1 cubic metre = 1000 litres)

  1. 60,000 litres

  2. 1,10,000 litres

  3. 3,45,400 litres

  4. 5,55,000 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The cylinder fits inside a sphere of radius 6. The cylinder's height is 10, so its radius r satisfies r^2 + (h/2)^2 = R_sphere^2. r^2 + 5^2 = 6^2, so r^2 = 36 - 25 = 11. Volume = pi * r^2 * h = 3.14159 * 11 * 10 = 345.57 cubic meters. 345.57 * 1000 = 345,570 litres. Option C is the closest.

Multiple choice

A right circular cylinder has a height of 15 units and a radius of 7 units. A rectangular solid with a height of 12 units and a square base is placed in the cylinder such that each of the corners of the solid is tangential to the cylinder wall. Liquid is then poured into the cylinder such that it reaches the rim. The volume of the liquid is

  1. 147(5 π - 8) unit3

  2. 180( π - 5) unit3

  3. 49( 5π - 24) unit3

  4. 49( 15π - 8) unit3
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of cylinder = pi * r^2 * h = pi * 49 * 15 = 735pi. The rectangular solid has a square base. If corners are tangential to the cylinder, the diagonal of the square base = diameter of cylinder = 14. Side of square = 14 / sqrt(2) = 7 * sqrt(2). Area of base = 98. Volume of solid = 98 * 12 = 1176. Liquid volume = 735pi - 1176 = 147(5pi - 8).