Mathematics · Class 10

Active learning ideas

Volumes of Cuboids and Cylinders

Active learning helps students visualise how volume works in real objects they see every day. When they measure classroom spaces or build model containers, the abstract formulas become concrete and meaningful for everyday uses like storage or water tanks.

• CBSE Learning Outcomes
• NCERT: Surface Areas and Volumes - Class 10

• 20–45 min
• Pairs → Whole Class
• 4 activities

Activity 01

• Experiential Learning
• 30 min · Pairs

Pairs Measurement: Classroom Volumes

Pairs select cuboid objects like books or boxes and cylindrical items like bottles. They measure dimensions with rulers, calculate volumes using formulas, and compare results. Discuss units and conversions to litres as a class.

Explain how the volume of a cuboid is a measure of the space it occupies.

Facilitation Tip

During Pairs Measurement, ensure pairs use the same measuring tape to avoid discrepancies and discuss why slight variations happen in real measurements.

What to look for

Present students with images of a cuboidal box and a cylindrical can. Ask them to write down the formula for the volume of each and identify one real-world item that resembles each shape.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 02

• Experiential Learning
• 45 min · Small Groups

Small Groups Build: Model Tanks

Groups construct cuboid and cylinder models from cardboard or clay. Measure and compute volumes before filling with sand or water to verify. Record discrepancies and refine measurements.

Differentiate between surface area and volume in practical applications.

Facilitation Tip

While Small Groups Build Model Tanks, remind groups to sketch dimensions first so they can plan how to divide the material before cutting.

What to look for

Give students a cuboid with dimensions 10 cm × 5 cm × 4 cm and a cylinder with radius 3 cm and height 7 cm. Ask them to calculate the volume of each and state which container holds more.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 03

• Experiential Learning
• 40 min · Whole Class

Whole Class Challenge: Capacity Problems

Project scenarios like filling a cylindrical drum or packing cuboid crates. Students solve in teams, present solutions, and vote on the most practical. Teacher facilitates formula application.

Construct a problem involving the capacity of a cylindrical container.

Facilitation Tip

For Whole Class Challenge, encourage students to explain their methods aloud so peers can learn from different approaches to the same problem.

What to look for

Pose the question: 'If you want to buy paint for a room (cuboid) versus buying oil to fill a drum (cylinder), what concept are you primarily concerned with for each, and why?' Guide them to differentiate between surface area and volume.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

Activity 04

• Experiential Learning
• 20 min · Individual

Individual Extension: Design a Container

Students design a cuboid or cylinder container for a given volume, like 100 litres of oil. Sketch, calculate dimensions, and explain choices. Share digitally or on posters.

Explain how the volume of a cuboid is a measure of the space it occupies.

Facilitation Tip

When students Design a Container individually, provide grid paper so they can accurately draw and label dimensions before calculating.

What to look for

Present students with images of a cuboidal box and a cylindrical can. Ask them to write down the formula for the volume of each and identify one real-world item that resembles each shape.

• Apply
• Analyze
• Evaluate
• Self-Awareness
• Self-Management
• Social Awareness

A few notes on teaching this unit

Teachers should start with tangible objects students recognise, like lunch boxes or water bottles, to ground the concept in familiar shapes. Avoid rushing to formulas; instead, let students derive the cylinder volume formula by comparing it to cuboids. Research shows hands-on measurement before abstract calculation builds stronger number sense and reduces formula memorisation without understanding.

Successful learning looks like students confidently distinguishing when to use volume formulas, measuring dimensions accurately, and explaining why these formulas matter in household or classroom contexts. They should connect calculations to practical problems like choosing between boxes or cans for storage.

---

Watch Out for These Misconceptions

• During Pairs Measurement, watch for students who confuse volume with surface area when measuring classroom spaces.

  Have pairs calculate both volume and surface area of the same cuboid space, then compare the numbers to see why volume is in cubic units and surface area is in square units. Ask them to share which measure matters more for storing books or furniture.

• During Small Groups Build Model Tanks, watch for groups using the diameter instead of the radius in cylinder volume calculations.

  Provide empty tin cans and string so groups can measure the diameter, then fold the string to find the radius. Ask them to recalculate using the radius and compare results to see why the formula requires radius squared.

• During Whole Class Challenge, watch for students approximating pi as 3 or 22/7 without justification.

  Set up a station with a measuring cylinder and water to let students fill a cylindrical container and compare their calculated volume using pi to the actual water volume. Discuss why approximations lead to measurable differences in capacity tasks.

---

Methods used in this brief

• Experiential Learning