Quantitative Aptitude

Mensuration of Solid Figures

147 Questions

Mensuration of solid figures deals with calculating the volume and surface area of 3D shapes. Common structures include cubes, cuboids, and rectangular prisms. These quantitative aptitude questions are standard in SSC, banking, and railway recruitment tests.

Cube volume formulasCuboid surface areaRectangular prismsDensity calculationsDimensional ratios

Mensuration of Solid Figures Questions

Multiple choice general knowledge math & puzzles

surface area of a cube

  1. 6 a*a

  2. 8 a*a

  3. 2 a*a

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

A cube has six identical square faces. If the side length is 'a', the area of one face is a*a. The total surface area is the sum of all six faces, which is 6 * a^2.

Multiple choice general knowledge math & puzzles

What is the volume of cuboid? (A) The lateral surface area of each face is 4,6,9. (B) Sum of the three dimensions (l,b,h) is 10 and the total surface area is 38

  1. The question can be answered by only one of the statements and not by the other statement

  2. The question can be answered by both statements individually

  3. The question can be answered by both statements together

  4. The question cannot be answered.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Statement A: lh = 4, bh = 6, lb = 9. Volume = lbh. From these: (lh)(bh)(lb) = l²b²h² = 4×6×9 = 216, so lbh = 6. Statement A alone is sufficient. Statement B: l + b + h = 10 and 2(lb + bh + lh) = 38. This gives lb + bh + lh = 19. With l+b+h=10 and sum of pairwise products=19, we can find (l+b+h)² = l²+b²+h²+2(lb+bh+lh), giving sum of squares = 100-38 = 62. But we cannot uniquely determine l, b, h from sum and sum of squares alone. Statement A alone suffices.

Multiple choice general knowledge math & puzzles

What is the surface area of a cube measuring 4 cm on an edge

  1. 64 cm squared

  2. 96 cm squared

  3. 16 cm squared

  4. 48 cm squared
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The surface area of a cube is calculated by the formula 6s^2, where s is the edge length. For a cube with edge 4 cm: 6 x (4 cm)^2 = 6 x 16 cm^2 = 96 cm^2. Option A (64 cm^2) would be the volume (4^3), option C (16 cm^2) is just s^2, and option D (48 cm^2) might result from incorrectly using 3s^2 instead of 6s^2.

Multiple choice

The length, breadth and height of a cuboid are 12 m, 6 m and 5 m, respectively. The cuboid is melted and converted into 10 equal cubes. In this process, 25% of the material is lost. How long will be the edge of each cube?

  1. 2 m

  2. 3 m

  3. 4 m

  4. 6 m

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

Volume of cuboid = 12*6*5 = 360 m3

Material lost = 25% of 360 = 90 m3

So, the remaining material = 360 – 90 = 270 m3

Now, the volume of each cube = 270/10 = 27 m3

So, a3 = 27

a = 3 m

So, the edge of each cube is 3 m.

Multiple choice

Boxes of 12 inches in height are stacked next to boxes of 16 inches height. At what minimum value will be the two stacks be of same height?

  1. 22 inches

  2. 28 inches

  3. 38 inches

  4. 48 inches
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find when the two stacks will be the same height, we need the least common multiple (LCM) of 12 and 16. The LCM of 12 and 16 is 48 inches, which means after 4 stacks of 12-inch boxes and 3 stacks of 16-inch boxes, both stacks reach 48 inches.

Multiple choice

The ratio of surface areas of 2 cubes is 1 : 9. Find the ratio of their volumes.

  1. 1 : 729

  2. 3 : 27

  3. 1 : 27

  4. 1 : 9
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the side of one cube is 2 cmThen surface area = 6 l2 = 6 x 2 x 2 = 24 cm2  Other cube's surface area will be 9 x 24 = 216 cm2

( as they are in ratio of 1: 9 ) 

now      6 l2 = 216              l2 = 216 / 6

               l2 = 36               l = 6volume of first cube  = side x side x side                                      = 2 x 2 x 2 = 8 cm3                                      volume of other cube = 6 x 6 x 6  = 216 cm3              Ratio = 8 / 216 = 1 / 27

       so ratio will be 1 : 27    

Multiple choice

If the bottom, side and front areas of a rectangular box are known, what will be the product of these areas?

  1. Volume of the box

  2. Square root of the volume

  3. Twice the volume

  4. Square of the volume

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

If the dimensions are designated by l, w and h, then the bottom, side and front areas are lw, wh and hl. The product of these areas = l2* w2* h2 = (lwh)2 = the square of the volume. So, option (4) is correct.