Volume and Surface Area of 3D Shapes - Class 8 Mensuration Worksheet PDF

Complete Class 8 mensuration worksheet with 24 problems on volume and surface area. Master cuboid, cube, cylinder, cone, sphere, and hemisphere formulas with real-world applications and step-by-step solutions.

Understanding Mensuration

Mensuration is the branch of mathematics that deals with the measurement of geometric figures - their length, area, volume, and surface area. It helps us calculate the space occupied by 2D and 3D objects.

Key Formulas for 3D Shapes

CUBOID (Rectangular Box):

• Volume = length × breadth × height = l × b × h
• Total Surface Area (TSA) = 2(lb + bh + hl)
• Lateral Surface Area (LSA) = 2h(l + b)

CUBE:

• Volume = side³ = a³
• Total Surface Area = 6a²
• Lateral Surface Area = 4a²

CYLINDER:

• Volume = πr²h
• Curved Surface Area = 2πrh
• Total Surface Area = 2πr(r + h)

CONE:

• Volume = ⅓πr²h
• Curved Surface Area = πrl (where l = slant height)
• Total Surface Area = πr(r + l)
• Slant Height: l = √(r² + h²)

SPHERE:

• Volume = 4/3 πr³
• Surface Area = 4πr²

HEMISPHERE:

• Volume = 2/3 πr³
• Curved Surface Area = 2πr²
• Total Surface Area = 3πr²

Important Note: Use π = 22/7 or π = 3.14 as specified in the problem.

Solved Example

Problem: A cylindrical water tank has a radius of 3.5 m and height of 6 m. Find the volume of water it can hold and the curved surface area. (Use π = 22/7)

Solution:

Given: Radius (r) = 3.5 m, Height (h) = 6 m, π = 22/7

Step 1: VolumeV = πr²hV = 22/7 × 3.5 × 3.5 × 6V = 22/7 × 12.25 × 6V = 231 m³

Step 2: Curved Surface AreaCSA = 2πrh = 2 × 22/7 × 3.5 × 6CSA = 132 m²

Understanding: A cylinder has two circular bases (top and bottom) and a curved surface. Volume tells us how much water it can hold (in cubic meters). Curved surface area is the area of the side wall.

Sample Practice Problems

Find the volume of a cube with side 5 cm.

A cuboid has dimensions: length = 8 cm, breadth = 6 cm, height = 4 cm. Find its volume.

The radius of a sphere is 7 cm. Find its surface area. (Use π = 22/7)

A hemispherical bowl has a radius of 3.5 cm. Find the volume of the bowl. (Use π = 22/7)

Word Problem: Priya wants to paint the four walls and ceiling of her room. The room is 5 m long, 4 m wide, and 3 m high. Find the total area to be painted.

A cone has a radius of 5 cm and a slant height of 13 cm. Find its curved surface area. (Use π = 3.14)

Picture-based Problem: A cylindrical pillar has radius 28 cm and height 3.5 m. How much concrete is needed to build it? (Use π = 22/7)

The total surface area of a cube is 384 cm². Find the length of its edge.

Real-life Problem: A metallic sphere of radius 4.2 cm is melted and recast into a cylinder of radius 6 cm. Find the height of the cylinder. (Use π = 22/7)

A tent is in the shape of a cylinder surmounted by a conical top. The height of the cylindrical part is 2.1 m and the total height is 4.2 m. The diameter of the base is 4 m. Find the total canvas required for the tent. (Use π = 22/7)

Complex Problem: A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical bottles of diameter 3 cm and height 4 cm. How many bottles are needed to empty the bowl?

Application Problem: A road roller has a cylindrical roller of diameter 84 cm and length 1 m. How much area will it press in 500 complete revolutions? Express your answer in m². (Use π = 22/7)

Scoring Guide

20-24 correct: Excellent! Outstanding! Move on to compound shapes, surface area of revolution, and coordinate geometry applications.

15-19 correct: Very Good! Great work! Practice more complex word problems involving combined shapes. Focus on conversion problems (sphere to cylinder, etc.).

10-14 correct: Good Effort! Keep practicing! Memorize all formulas on flashcards. Practice 10 problems daily, starting with basic shapes before combined shapes.

0-9 correct: Keep Trying! Review formulas carefully. Start with cube and cuboid, then move to cylinder. Practice finding volume and surface area separately before mixing them.

Tips for Improvement

Create a formula sheet: Write all formulas on one page and keep it visible while studying

Visualize shapes: Draw diagrams for every problem - it helps understand what's being asked

Unit conversion: Always convert all measurements to the same unit before calculating

Check units in answer: Area is always in square units (cm², m²), volume in cubic units (cm³, m³)

Use π wisely: Use 22/7 for exact answers, 3.14 when specified

Word problems strategy: Identify the shape → Write given values → Choose correct formula → Calculate

Combined shapes: Break them into simpler shapes and add/subtract volumes or areas

Common Mistakes to Avoid

Using diameter instead of radius (remember: radius = diameter ÷ 2)

Forgetting to square or cube when required (r² means r × r, not 2 × r)

Mixing up TSA, LSA, and CSA - read questions carefully

Not converting units (mixing cm and m in same calculation)

Confusing volume formulas (especially cone = ⅓ × cylinder)

Forgetting to multiply by π in circular shapes

Wrong formula for hemisphere (it's 2/3 πr³, not 1/3 or 4/3)

In combined shapes, counting the common base twice in surface area

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