Volume and Surface Area – Solid Figures Aptitude Questions & Answers, Important Topics!!

Solid Figures

Anything that occupies space is called a Solid. With Area, a solid figure has Volume also. Length, Breadth, and Height are three dimensions.

CUBOID

Let length = l, breadth = b and height = h units. Then

  1. Volume = (l x b x h) cubic units.
  2. Surface area = 2(lb + bh + lh) sq. units.
  3. Diagonal = Square root of l2 + b2 + h2 units.

CUBE

Let each edge of a cube be of length a. Then,

  1. Volume = a3 cubic units.
  2. Surface area = 6a2 sq. units.
  3. Diagonal = square root of 3a units.

CYLINDER

Let radius of base = r and Height (or length) = h. Then,

  1. Volume = (pi r2h) cubic units.
  2. Curved surface area = (2 pi rh) sq. units.
  3. Total surface area = 2 pi r(h + r) sq. units.

CONE

Let radius of base = r and Height = h. Then,

  1. Slant height, l = h2 + r2 units.
  2. Volume = [1/3 pi r2h] cubic units.
  3. Curved surface area = (pirl) sq. units.
  4. Total surface area = (pirl + pir2) sq. units

SPHERE

Let the radius of the sphere be r. Then,

  1. Volume = 4/3 pi r3 cubic units.
  2. Surface area = (4pir2) sq. units.

HEMISPHERE

Let the radius of a hemisphere be r. Then,

  1. Volume = 2/3 pi r3 cubic units.
  2. Curved surface area = (2 pi r2) sq. units.
  3. Total surface area = (3 pi r2) sq. units.Note: 1 litre = 1000 cm3.

Volume and Surface Area of Solid Figures Aptitude Moderate Questions and Answers

1. The surface area of a cube is 726 m2. Is its volume?

  • A. 1300 m3
  • B. 1331 m3
  • C. 1452 m3
  • D. 1542 m3

Answer: Option B (1331 m3)

2. Three-sided metal cubes of 5 cm, 4 cm, and 3 cm will be melted and recast into a new cube. The edge length of that cube, is it?

  • A. 6 cm
  • B. 8 cm
  • C. 10 cm
  • D. None of these

Answer: Option A (6 cm)

3. What is the maximum number of pieces of 5 cm x 5 cm x 10 cm cake that can be cut from a 5 cm x 30 cm x 30 cm large cake?

  • A. 10
  • B. 15
  • C. 18
  • D. 30

Answer: Option C (18)

4. 5 cm of rainfall, in a shower. The volume of water falling on 1.5 hectares of land is as follows:

  • A. 75 cu. m
  • B. 750 cu. m
  • C. 7500 cu. m
  • D. 75000 cu. m

Answer: Option B (750 cu. m)

5. A hall is 15 m long and 12 m wide. If the sum of the floor and ceiling areas is equal to the sum of the four wall surfaces, the hall volume is:

  • A. 720
  • B. 900
  • C. 1200
  • D. 1800

Answer: Option C (1200)

6. A hollow iron pipe is 21 cm long, with an outer diameter of 8 cm. If the pipe thickness is 1 cm and iron weighs 8 g / cm3, then the pipe weight is:

  • A. 3.6 kg
  • B. 3.696 kg
  • C. 36 kg
  • D. 36.9 kg

Answer: Option B (3.696 kg)

7. A boat measuring 3 m in length and 2 m in breadth floats on a lake. When a man gets on it, the boat sinks by 1 cm. The Mass of the Man is:

  • A. 12 kg
  • B. 60 kg
  • C. 72 kg
  • D. 96 kg

Answer: Option B (60 kg)

8. A 6 m long and 4 m wide cistern contains water that reaches a depth of 1 m 25 cm. The total wet surface area is

  • A. 49 m2
  • B. 50 m2
  • C. 53.5 m2
  • D. 55 m2

Answer: Option A (49 m2)

9. A capacity cistern of 8000 liters measures 3.3 m by 2.6 m by 1.1 m externally, and its walls are 5 cm thick. The bottom thickness is:

  • A. 90 cm
  • B. 1 dm
  • C. 1 m
  • D. 1.1 cm

Answer: Option B ( 1 dm)

10. A large cube is formed by melting three smaller cubes of 3, 4, and 5 cm sides from the material obtained. What is the ratio of the smaller cube’s total surface area with the larger cube?

  • A. 2: 1
  • B. 3: 2
  • C. 25: 18
  • D. 27: 20

Answer: Option C (25: 18)

Leave a Reply

Your email address will not be published. Required fields are marked *

Nature's Inspiration

Quote of the day!

__________________

Knowing is not enough; we must apply.
Wishing is not enough; we must do.

All rights reserved. Privacy Policy Privacy Policy