## 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

*Volume*= (*l*x*b*x*h*) cubic units.*Surface area*= 2(*lb*+*bh*+*lh*) sq. units.*Diagonal*= Square root of*l*^{2}+*b*^{2}+*h*^{2}units.

**CUBE**

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

*Volume*=*a*^{3}cubic units.*Surface area*= 6*a*^{2}sq. units.*Diagonal*= square root of 3*a*units.

**CYLINDER**

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

*Volume*= (pi*r*^{2}*h*) cubic units.*Curved surface area =*(2 pi*rh*) sq. units.*Total surface area*= 2 pi*r*(*h*+*r*) sq. units.

*CONE*

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

*Slant height,**l*=*h*^{2}+*r*^{2}units.*Volume*= [1/3 pi*r*^{2}*h]*cubic units.*Curved surface area*= (pi*rl*) sq. units.*Total surface area*= (pi*rl*+ pi*r*^{2}) sq. units

**SPHERE**

Let the radius of the sphere be *r*. Then,

*Volume*= 4/3 pi*r*^{3 }cubic units.*Surface area*= (4pi*r*^{2}) sq. units.

**HEMISPHERE**

Let the radius of a hemisphere be *r*. Then,

*Volume*= 2/3 pi*r*^{3 }cubic units.*Curved surface area*= (2 pi*r*^{2}) sq. units.*Total surface area*= (3 pi*r*^{2}) sq. units.Note: 1 litre = 1000 cm^{3}.

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

**1. The surface area of a cube is 726 m ^{2}. Is its volume?**

- A. 1300 m
^{3} - B. 1331 m
^{3} - C. 1452 m
^{3} - D. 1542 m
^{3}

**Answer:** Option B (1331 m^{3})

**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)