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 ratio of the radius of the base to the height of a cone is 5 : 12. If the cost of smoothening the curved surface area (CSA) is Rs. 115.50 at a rate of 5 paise per sq. cm, then what is the total surface area of the cone?

  1. 3696.36 cm2

  2. 3693 cm2

  3. 3198.46 cm2

  4. 3332 cm2
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Ratio r:h = 5:12, so r=5k, h=12k, slant height l=13k. CSA = pi*r*l = pi*5k*13k = 65*pi*k^2. Cost = 115.50 / 0.05 = 2310 sq cm. 65*pi*k^2 = 2310. k^2 = 2310 / (65*3.14) = 11.31. k = 3.36. Total surface area = pi*r*(r+l) = pi*5k*(18k) = 90*pi*k^2 = 90 * 3.14 * 11.31 = 3198.46.

Multiple choice

A solid vessel of cylindrical shape, having volume of 33.264 litres, is cast into a conical shape of height 72 cm. What is the cost of painting its CSA at Rs. 12 per sq. m?

  1. Rs. 5.94

  2. Rs. 6.94

  3. Rs. 7.95

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

Volume of cylinder = 33.264 liters = 0.033264 m^3. Converted to cm^3, it is 33264 cm^3. Using V = (1/3) * pi * r^2 * h, we find r = 21 cm. The slant height l = sqrt(r^2 + h^2) = sqrt(21^2 + 72^2) = 75 cm. CSA = pi * r * l = (22/7) * 21 * 75 = 4950 cm^2 = 0.495 m^2. Cost = 0.495 * 12 = 5.94.

Multiple choice

The volume of a spherical balloon is increasing at the rate of 20 cm3/s. The rate of change of its surface area at the instant when its radius is 8 cm is:

  1. 5 cm2/s

  2. 10 cm2/s

  3. 4 cm2/s

  4. 2.5 cm2/s
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume V = (4/3)*pi*r^3. dV/dt = 4*pi*r^2 * dr/dt = 20. At r=8, 4*pi*64 * dr/dt = 20, so dr/dt = 20 / (256*pi) = 5 / (64*pi). Surface area S = 4*pi*r^2. dS/dt = 8*pi*r * dr/dt. Substituting: dS/dt = 8*pi*8 * (5 / (64*pi)) = 64*pi * (5 / (64*pi)) = 5 cm^2/s.

Multiple choice

The total area of a circle and a square is 2611 sq. cm. The diameter of the circle is 42 cm. What is the sum of the circumference of the circle and the perimeter of the square?

  1. 272 cm

  2. 380 cm

  3. 280 cm

  4. 294 cm

  5. 270 cm
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Diameter = 42, Radius = 21. Area of circle = (22/7) * 21 * 21 = 1386. Area of square = 2611 - 1386 = 1225. Side of square = sqrt(1225) = 35. Circumference of circle = 2 * (22/7) * 21 = 132. Perimeter of square = 4 * 35 = 140. Sum = 132 + 140 = 272.

Multiple choice

The volume of a solid cone is exactly equal to the total volume of three smaller cones, each with radius 4 cm and height 7 cm. What is the height of the larger cone if its radius is same as that of a smaller cone?

  1. 8 cm

  2. 6 cm

  3. 15 cm

  4. 21 cm

  5. 14 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of 3 small cones = 3 * (1/3 * pi * 4^2 * 7) = pi * 16 * 7 = 112 * pi. Volume of large cone = 1/3 * pi * 4^2 * H = 16/3 * pi * H. Equating: 16/3 * pi * H = 112 * pi. H = 112 * 3 / 16 = 7 * 3 = 21.

Multiple choice

A cylindrical water tank is open at the top. Its curved surface area is 396 m2. The height of the tank is 21 m. Ignoring the thickness of the material used for building the tank, find the total cost of painting the outer surfaces of the tank at the rate of Rs. 14 per m2 if the outer bottom part of the tank is also included.

  1. Rs. 4,050

  2. Rs. 5,940

  3. Rs. 6,950

  4. Rs. 5,500

  5. Rs. 6,500
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Curved Surface Area = 2*pi*r*h = 396. With h=21, 2*pi*r*21 = 396, so r = 396 / (42*pi) = 3 m. The total area to paint is CSA + Area of base = 396 + pi*r^2 = 396 + 9*pi. Using pi approx 22/7, 396 + 9*(22/7) = 396 + 28.28 = 424.28. Cost = 424.28 * 14 = 5940.