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CSEEL (Center for Scientific Exploration and Experiential Learning) is a premier Indian STEM educational initiative offering hands-on science experiments, 3D live laboratory simulations, curriculum-aligned project kits, teacher training workshops, and national science conclaves aligned with NEP 2020.

How does CSEEL support NEP 2020 experiential learning?

CSEEL shifts education from rote memorization to active inquiry and hands-on experimentation. Students observe, build, analyze, and apply scientific concepts to real-world challenges, developing critical thinking and scientific temper as envisioned by NEP 2020.

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CSEEL provides comprehensive physics, chemistry, biology, environmental science, and applied robotics experiments and virtual simulations for students from Class 6 through Class 12, mapped to CBSE, ICSE, and state curricula.

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Surface Area & Volume Relationships: Sphere, Cone, and Cylinder

Experiment video

What you will learn

Verify Archimedes' ratio of volumes and surface areas between a cone, a sphere, and a cylinder having identical radius (r) and height (h = 2r) using dry fine sand displacement.

Materials needed

Hollow transparent acrylic geometric models: Cylinder (radius r = 5 cm, height h = 10 cm), Sphere (radius r = 5 cm with top aperture), Cone (radius r = 5 cm, height h = 10 cm) set
Hollow transparent acrylic geometric models: Cylinder (radius r = 5 cm, height h = 10 cm), Sphere (radius r = 5 cm with top aperture), Cone (radius r = 5 cm, height h = 10 cm) set
₹50
What is it?
Set of hollow transparent acrylic geometric solids sharing identical radius r = 50 mm and height h = 100 mm.
Specifications
Solids Included
Right circular cone, cylinder, full sphere, hemisphere
Wall Thickness
2.5 mm optical clear acrylic
Lid Openings
Removable fill caps on all bases
Calibration
Exact 1:2:3 volumetric ratio matched
Fine dry colored sand or water kg
Fine dry colored sand or water kg
₹95
What is it?
Fine dry quartz test sand (graded mesh 50-70) colored with non-toxic pigment.
Specifications
Particle Size
0.2 – 0.3 mm uniform quartz grains
Flowability
Free-flowing dry granular bulk density 1.55 g/cm³
Quantity
2.0 kg in plastic pour container
Measuring Flask (1000 mL)
Measuring Flask (1000 mL)
₹140
What is it?
Graduated 1000 mL Class A measuring cylinder for volumetric liquid cross-check.
Specifications
Capacity
1000 mL
Graduation
10 mL subdivisions
Material
Polypropylene chemical/shatter resistant
Plastic funnel and collection tray
Plastic funnel and collection tray
₹185
What is it?
Standard laboratory apparatus used in Surface Area & Volume Relationships: Sphere, Cone, and Cylinder.
Specifications
Category
Mathematics Apparatus
Grade
CBSE / NEP 2020 Laboratory Standard
Leveling straightedge ruler
Leveling straightedge ruler
₹230
What is it?
Standard laboratory apparatus used in Surface Area & Volume Relationships: Sphere, Cone, and Cylinder.
Specifications
Category
Mathematics Apparatus
Grade
CBSE / NEP 2020 Laboratory Standard

Tick items as you collect them. Tap + to see the product, specifications and buy options.

Stay safe

Ensure sand is completely dry and free of clumps to ensure uniform packing density.
Always level the sand rim with a flat straightedge; avoid packing or shaking vigorously between fills.
Pour sand through a funnel slowly into the models to avoid spilling outside the measurement rim.
Wipe acrylic models with anti-static cloth to prevent sand grains sticking to walls.

Steps

0 of 7 steps done

1Verify dimensions of acrylic solids: cylinder height h = 10 cm, radius r = 5 cm; cone height h = 10 cm, radius r = 5 cm; sphere diameter 2r = 10 cm.
Observation
Inspect hollow transparent plastic shapes: cone, hemisphere, sphere, and cylinder sharing identical radius r = 5.0 cm and height h = 10.0 cm.
Safety
Check plastic shapes for cracks or leaks before filling with liquid/sand.
2Fill the hollow cone completely with fine sand and level off flush with the rim using a straightedge.
Observation
Fill hollow cone to the brim with fine colored dry sand; level top surface with a straight ruler edge.
Safety
Pour sand over plastic tray to catch any spills.
3Pour the sand from the cone into the empty cylinder. Observe that it fills exactly 1/3 of the cylinder's volume.
Observation
Pour sand from cone into cylinder: exactly one-third of cylinder is filled.
Safety
Tap cylinder base lightly to settle sand evenly.
4Fill the cone two more times into the cylinder: three full cones exactly fill the cylinder (V_cylinder = 3 × V_cone = 3 × (1/3 πr²h) = πr²h).
Observation
Pour second full cone of sand into cylinder: cylinder is now two-thirds full.
Safety
Ensure cone is filled completely flush with brim each time.
5Now empty the cylinder. Fill the hollow sphere model with fine sand.
Observation
Pour third cone of sand into cylinder: sand reaches the absolute brim of the cylinder, proving V(Cylinder) = 3 × V(Cone).
Safety
Zero sand remains left over; cylinder is filled to 100% capacity.
6Pour the sphere's sand into the empty cylinder: it fills exactly 2/3 of the cylinder (V_sphere = 2/3 V_cylinder = 4/3 πr³).
Observation
Fill hollow sphere with 2 full measures of the cone, proving V(Sphere) = 2/3 V(Cylinder) = 4/3 πr³.
Safety
Return dry sand to storage hopper and wipe transparent models with microfiber cloth.
7Combine one full cone of sand and one full sphere of sand: together they fill the cylinder 100% full.

Tap + on a step to see what you will observe and any safety tips.

Record your observations

Geometric Solid Body	Theoretical Formula (h = 2r = 10 cm)	Volume Calculated (cm³)	Sand Filling Measure (Scoops)	Volume Ratio to Cylinder
Cone (r = 5 cm, h = 10 cm)	V = 1/3 · π · r² · h = 1/3 × π × 25 × 10	261.80 cm³	1 scoop (Base unit 1.0)	1 / 3 (33.3% of cylinder)
Sphere (r = 5 cm, d = 10 cm)	V = 4/3 · π · r³ = 4/3 × π × 125	523.60 cm³	2 scoops (Exactly 2× cone)	2 / 3 (66.7% of cylinder)
Cylinder (r = 5 cm, h = 10 cm)	V = π · r² · h = π × 25 × 10	785.40 cm³	3 scoops (Exactly 3× cone)	3 / 3 (100% full capacity)

Tap a highlighted cell to write your own observation.

Result and conclusion

Empirically verified that Volume of Cone : Volume of Sphere : Volume of Cylinder = 1 : 2 : 3. Sand from one cone and one sphere exactly fills the circumscribed cylinder without spill.

V(Cone) : V(Sphere) : V(Cylinder) = (1/3 · πr²h) : (4/3 · πr³) : (πr²h) = 1 : 2 : 3 (for h = 2r)

Observation	What it means
Archimedes Epitaph Ratio 1:2:3	Archimedes regarded this discovery as his crowning triumph: for a cylinder circumscribed around a sphere and cone (h = 2r), their volumes are strictly 1 : 2 : 3.
Experimental Volumetric Proof	Exactly 3 full measures of the cone fill the cylinder to the brim (V_cyl = 3 · V_cone).
Sphere to Cone Equivalence	Pouring 2 full measures of the cone fills the hollow sphere completely (V_sphere = 2 · V_cone = 4/3 πr³).
Surface Area Relationship	Total surface area of sphere (4πr²) equals the curved surface area of the circumscribed cylinder (2πr·h = 2πr·2r = 4πr²).

Volumetric Relationship: Cone vs Sphere vs Circumscribed Cylinder

Sample readings. Replace with your own results.

Experiment photos

Before the experimentDuring the experimentResult