## 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

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

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

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

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

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

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

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

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