Moderate Level Worksheet

Part A: Subjective Questions - Very Short Answer (1 Mark Each)

In this moderate level, we'll work with more complex problems involving conversions, finding unknown dimensions, and cost calculations.

These skills are essential for practical applications in engineering and construction.

1. Define total surface area.

Total surface area is the sum of areas of all facesthe volume of a solid.

Perfect! It includes all outer surfaces of a 3D shape.

2. Write the formula for the curved surface area of a cylinder.

CSA = 2πrhπr²h

Excellent! Curved surface area = 2π × radius × height.

3. What is the relation between 1 m³ and cm³?

1 m³ = 10000001000 cm³

Correct! 1 m = 100 cm, so 1 m³ = 100 × 100 × 100 = 1,000,000 cm³.

4. Write the formula for the volume of a cube in terms of side.

Volume = a³6a²

Great! Volume = side³.

5. Write the total surface area of a cuboid.

TSA = 2(lb + bh + hl)l × b × h

Perfect! Total surface area includes all 6 rectangular faces.

Drag each problem type to its solution approach:

Part A: Section B – Short Answer Questions (2 Marks Each)

1. Find the total surface area of a cuboid with length 15 cm, breadth 8 cm, and height 5 cm.

TSA = 2(lb + bh + hl)2(l + b)

= 2( × + × + × )

= 2( + + )

= 2 × = cm²

Excellent! Total surface area = 470 cm².

2. The diameter of a cylinder is 10 cm and its height is 14 cm. Find its curved surface area.

Diameter = 10 cm, so radius = cm

CSA = 2πrh = 2 × × ×

= cm² (approximately)

Perfect! Curved surface area ≈ 440 cm².

3. Find the volume of a cuboid whose dimensions are 9 cm × 8 cm × 7 cm.

Volume = l × b × h = × ×

= cm³

Great! Volume = 504 cm³.

4. The edge of a cube is 12 cm. Find its total surface area and volume.

Total Surface Area = 6a² = 6 × ()² = 6 × = cm²

Volume = a³ = ()³ = cm³

Excellent! TSA = 864 cm² and Volume = 1728 cm³.

5. Find the height of a cylinder whose volume is 5544 cm³ and radius is 7 cm.

Volume = πr²h

5544 = × ² × h

5544 = 3.14 × 49 × h = × h

h = 5544 ÷ 153.86 = cm

Perfect! Height = 36 cm.

Part A: Section C – Long Answer Questions (4 Marks Each)

1. A rectangular tank is 80 cm long, 40 cm wide, and 30 cm deep. Find: (a) Its volume, and (b) The cost of painting its inner surface at ₹5 per m².

(a) Volume:

Volume = l × b × h2(l + b) = × ×

= cm³ = m³

Volume = 96,000 cm³ or 0.096 m³.

(b) Cost of painting:

Inner surface area (5 faces, no top) = lb + 2(bh + hl)

Convert to meters: l = m, b = m, h = m

Area = (0.8 × 0.4) + 2(0.4 × 0.3 + 0.3 × 0.8)

= + 2( + ) = 0.32 + 2 ×

= 0.32 + 0.72 = m²

Cost = 1.04 × 5 = ₹

Excellent! Cost = ₹5.20.

2. Find the total surface area of a cylinder of height 20 cm and base radius 7 cm.

TSA = 2πr(r + h)

= 2 × × × ( + )

= 2 × 3.14 × 7 ×

= cm² (approximately)

Perfect! Total surface area ≈ 1187 cm².

3. The dimensions of a cuboid are in the ratio 4 : 3 : 2 and its volume is 192 cm³. Find its dimensions.

Let dimensions be 4x, 3x, and 2x

Volume = 4x × 3x × 2x = x³ = 192

x³ = 192 ÷ 24 =

x = cm

Dimensions: Length = 4 × 2 = cm

Breadth = 3 × 2 = cm

Height = 2 × 2 = cm

Excellent! Dimensions are 8 cm × 6 cm × 4 cm.

4. A metal cube of edge 10 cm is melted to make 10 small cubes of equal size. Find the edge of each small cube.

Volume of large cube = ³ = cm³

Volume of each small cube = 1000 ÷ = cm³

If edge of small cube = a, then a³ =

a = ³√100 ≈ cm

Perfect! Edge of each small cube ≈ 4.64 cm.

Part B: Objective Questions - Test Your Knowledge!

Answer these multiple choice questions:

6. The total surface area of a cube with edge a =

(a) 4a² (b) 5a² (c) 6a² (d) None

Correct! 6 faces × a² each = 6a².

7. Lateral surface area of cuboid =

(a) 2(l + b)h (b) l × b × h (c) 2(lb + bh + hl) (d) None

Perfect! LSA = 2(l + b)h = perimeter of base × height.

8. The volume of cuboid having l = 10 cm, b = 8 cm, h = 5 cm is:

(a) 400 cm³ (b) 800 cm³ (c) 200 cm³ (d) 1000 cm³

Excellent! Volume = 10 × 8 × 5 = 400 cm³.

9. The formula to find the total surface area of cylinder is:

(a) 2πr² + 2πrh (b) 2πr²h (c) πr²h (d) None

Perfect! TSA = 2 circular areas + curved surface = 2πr² + 2πrh.

10. The height of a cylinder whose radius is 7 cm and volume 1540 cm³ =

(a) 10 cm (b) 8 cm (c) 6 cm (d) 12 cm

Correct! h = V ÷ (πr²) = 1540 ÷ (3.14 × 49) ≈ 10 cm.

🎉 Outstanding Work! You've Mastered Intermediate Surface Area and Volume!

Here's what you learned:

• Advanced Formula Applications:

  • Finding unknown dimensions from volume
  • Reverse calculations (height from volume and radius)
  • Cost calculations based on surface area
  • Ratio problems with dimensions

• Important Conversions:

  • 1 m³ = 1,000,000 cm³ (= 10⁶ cm³)
  • 1 m = 100 cm
  • 1 litre = 1000 cm³
  • Area: 1 m² = 10,000 cm²

• Complete Formulas:

  Cube:

  • TSA = 6a²
  • LSA = 4a²
  • Volume = a³

  Cuboid:

  • TSA = 2(lb + bh + hl)
  • LSA = 2(l + b)h
  • Volume = l × b × h

  Cylinder:

  • TSA = 2πr(r + h) = 2πr² + 2πrh
  • CSA = 2πrh
  • Volume = πr²h

• Problem-Solving Strategies:

  1. Identify what's given and what's asked
  2. Convert units if necessary
  3. Choose appropriate formula
  4. Rearrange formula for unknown variable
  5. Substitute and calculate
  6. Check units in answer

• Real-World Applications:

  • Painting costs (use surface area)
  • Water tank capacity (use volume)
  • Material requirements (use surface area)
  • Storage calculations (use volume)

• Key Techniques:

  • Ratio problems: Use variables (x) for unknown factor
  • Reverse calculations: Rearrange formulas
  • Inner surface area: Exclude top face for open containers
  • Cost calculations: Area × rate per unit area

These skills are essential for engineering, architecture, and everyday problem-solving!