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

Let A and B be two solid spheres, such that the surface area of B is 300% more than that of A. The volume of A is found to be k% lower than that of B. The value of k must be

  1. 85.5

  2. 92.5

  3. 90.5

  4. 87.5

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

Surface area S = 4 * pi * r^2. If S_B = 4 * S_A, then r_B^2 = 4 * r_A^2, so r_B = 2 * r_A. Volume V = (4/3) * pi * r^3. V_B = (4/3) * pi * (2 * r_A)^3 = 8 * V_A. The volume of A is 7/8 of V_B, which is 87.5% lower.

Multiple choice

The curved surface area and the total surface area of a cylinder are in the ratio 1 : 2. If the total surface area of the right cylinder is 616 cm2, then its volume is

  1. 1232 cm3

  2. 1848 cm3

  3. 1632 cm3

  4. 1078 cm3
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. Ratio CSA/TSA = 1/2 implies 2*pi*r*h = 2*pi*r^2, so h = r. TSA = 2*pi*r^2 + 2*pi*r^2 = 4*pi*r^2 = 616. r^2 = 616 / (4 * 22/7) = 49. r = 7, h = 7. Volume = pi*r^2*h = (22/7) * 49 * 7 = 1078.

Multiple choice

The total area of a circle and a rectangle is equal to 1166 sq.cm. If the length of the rectangle is 25 cm and the diameter of the circle is 28 cm, what is the sum of the circumference of the circle and the perimeter of the rectangle?

  1. 180 cm

  2. 182 cm

  3. 184 cm

  4. 186 cm

  5. 191 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area of circle = pi * r^2 = 22/7 * 14 * 14 = 616. Area of rectangle = 1166 - 616 = 550. Length = 25, so width = 550 / 25 = 22. Circumference = 2 * 22/7 * 14 = 88. Perimeter = 2 * (25 + 22) = 94. Sum = 88 + 94 = 182.

Multiple choice

Curved surface area and total surface area of a cone are in ratio 13 : 18. What is the ratio of height to radius of the cone?

  1. 6 : 13

  2. 10 : 13

  3. 12 : 5

  4. 13 : 5

  5. 15 : 13
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Curved surface area is pi*r*l and total surface area is pi*r(l+r). The ratio pi*r*l / pi*r(l+r) = l / (l+r) = 13/18. This implies 18l = 13l + 13r, so 5l = 13r, or l/r = 13/5. Using l^2 = h^2 + r^2, we find h^2 = l^2 - r^2 = (13r)^2/25 - r^2 = 144r^2/25, so h/r = 12/5.