Combined Hemisphere & Cylinder

Interactive geometry — Volume & Surface Area of a Combined Solid (Hemisphere on Cylinder)

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Radius: 2.0

Cyl. Height: 3.0

Measurements

Total Volume:54.45 units³

Cylinder Volume:37.70 units³

Hemisphere Volume:16.76 units³

Total Surface Area:75.40 units²

Formulas

Cylinder Volume (V_c) = πr²h

Hemisphere Volume (V_h) = (2/3)πr³

Total Volume (V) = V_c + V_h

Cylinder CSA = 2πrh

Hemisphere CSA = 2πr²

Total Surface Area = πr² + 2πrh + 2πr²

TSA Simplified = 3πr² + 2πrh

How to Use

• Drag to rotate the combined solid in 3D

• Scroll to zoom in / out

• Adjust sliders to change dimensions

• Watch measurements update in real-time

Key Terms

Combined Solid — a 3D shape made by joining two or more basic solids

Cylinder — the lower part with a circular base

Hemisphere — half a sphere forming the domed top

Great Circle — the circular face where hemisphere meets cylinder

Did You Know?

Combined solids with a hemisphere on a cylinder appear everywhere — grain silos with domed roofs, water storage tanks, pill capsules, domed stadiums, and pressure vessels. This shape maximizes internal volume while distributing stress evenly across the curved top!