Mensuration Word Problems

Mensuration word problems help students understand how geometry is used in real life. These problems involve calculating the area, surface area, and volume of different shapes such as cubes, cuboids, cylinders, and trapeziums.You may come across situations like painting walls, filling water tanks, covering boxes, or measuring land. To solve these, you must identify the shape correctly and apply the right formula. This chapter brings together all the important concepts of mensuration in one place and helps you solve mixed word problems step by step.

Table of Contents

• What are Mensuration Word Problems?
• Important Mensuration Formulas
• Solved Examples
• Real-Life Applications
• Key Points to Remember
• Practice Questions

What are Mensuration Word Problems?

Mensuration word problems are practical questions where you use geometry formulas to find the following:

• Area
• Surface Area
• Volume

These problems are based on everyday situations, like:

• Painting a room
• Filling a tank
• Wrapping a box
• Measuring a field

Key Idea: First identify the shape, then apply the correct formula.

Read more: Important Questions on Mensuration - Class 8

Important Mensuration Formulas

Here are the key formulas used in Class 8:

• Area of trapezium = ½ × (sum of parallel sides) × height
• Area of rhombus = ½ × d₁ × d₂
• Area of quadrilateral = ½ × diagonal × (sum of perpendiculars)
• Surface area of cube = 6a²
• Surface area of cuboid = 2(lb + bh + lh)
• Lateral surface area of cuboid = 2h(l + b)
• Surface area of cylinder = 2πr(r + h)
• Volume of cube = a³
• Volume of cuboid = l × b × h
• Volume of cylinder = πr²h

Solved Examples

Example 1: A room has a length of 10 m, a width of 5 m, and a height of 3 m. It has one door of 2 m × 1 m and one window of 1.5 m × 1 m. Find the cost of painting at Rs 20 per m².

Solution:

Lateral surface area = 2h(l + b)
= 2 × 3 × (10 + 5)
= 6 × 15 = 90 m²

Area of door = 2 × 1 = 2 m²
Area of window = 1.5 × 1 = 1.5 m²

Painted area = 90 − 2 − 1.5 = 86.5 m²

Cost = 86.5 × 20 = Rs 1,730

Answer: Rs 1,730

Example 2: A cylindrical tank has a radius of 1 m and a height of 3 m. Find its capacity in litres.

Solution:

Volume = πr²h
= 22/7 × 1 × 1 × 3
= 66/7 = 9.43 m³

Convert to litres:
9.43 × 1000 = 9,430 litres

Answer: 9,430 litres

Example 3: A box measures 25 cm × 15 cm × 10 cm. Find the wrapping paper required.

Solution:

Surface area = 2(lb + bh + lh)
= 2(25×15 + 15×10 + 25×10)
= 2(375 + 150 + 250)
= 2 × 775 = 1550 cm²

Answer: 1550 cm²

Example 4: Parallel sides are 30 m and 20 m; height is 8 m.

Solution:

Area = ½ × (a + b) × h
= ½ × (30 + 20) × 8
= ½ × 50 × 8 = 200 m²

Answer: 200 m²

Example 5: Find the sheet needed to make 10 cubes of side 1 m.

Solution:

Surface area of one cube = 6a²
= 6 × 1² = 6 m²

For 10 cubes = 10 × 6 = 60 m²

Answer: 60 m²

Example 6: Diagonals = 10 cm and 6 cm. Find the area of 20 tiles.

Solution:

Area of one tile = ½ × d₁ × d₂
= ½ × 10 × 6 = 30 cm²

Total = 20 × 30 = 600 cm²

Answer: 600 cm²

Example 7: Tank size = 3 m × 2 m × 1 m. Water fills at 2 litres/sec.

Solution:

Volume = 3 × 2 × 1 = 6 m³ = 6000 litres

Time = 6000 ÷ 2 = 3000 sec
= 50 minutes

Answer: 50 minutes

Example 8: Painting a Cylinder. Radius = 0.5 m, height = 4 m, rate = Rs 15/m²

Solution:

Curved surface area = 2πrh
= 2 × 22/7 × 0.5 × 4 = 88/7 ≈ 12.57 m²

Cost = 12.57 × 15 ≈ Rs 189

Answer: Rs 189

Real-Life Applications

Mensuration is used in many areas:

• Construction: Calculating paint, cement, and tiles
• Water Storage: Finding tank capacity
• Packaging: Designing boxes and containers
• Agriculture: Measuring land area
• Manufacturing: Estimating materials

Key Points to Remember

• Always identify the shape first
• Choose the correct formula
• Convert units when needed
• Use:
  • 1 m³ = 1000 litres
  • 1 litre = 1000 cm³
• Read carefully:
  • Surface area or lateral surface area?
• Use π = 22/7 unless it is mentioned

Practice Questions

1. A cuboid tank measures 5 m × 4 m × 3 m. Find its volume in litres.
2. Find the area of a trapezium with sides 50 m and 30 m and height 15 m.
3. A cylinder has a radius of 2 m and a height of 5 m. Find its volume.
4. Find the cost of painting a room (6 m × 5 m × 3 m) at Rs 25/m².
5. A cube has a surface area of 384 cm². Find its side length and volume.
6. A cylinder of height 7 m and diameter 2 m is filled with water. Find capacity.