Combined Hemisphere & Cone

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

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Radius: 2.0

Cone Height: 3.0

Measurements

Total Volume:37.70 units³

Cone Volume:12.57 units³

Hemisphere Volume:16.76 units³

Total Surface Area:62.83 units²

Slant Height:3.61 units

Formulas

Cone Volume (V_c) = ⅓πr²h

Hemisphere Volume (V_h) = (2/3)πr³

Total Volume (V) = V_c + V_h

Cone CSA = πrl (l = slant height)

Hemisphere CSA = 2πr²

Total Surface Area = πr² + πrl + 2πr²

TSA Simplified = 3πr² + πrl

Slant Height (l) = √(r² + h²)

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

Cone — the lower part tapering from the circular joint down to an apex

Hemisphere — half a sphere forming the domed top

Slant Height (l) — distance from apex to base edge of the cone

Did You Know?

The combined solid of a hemisphere on a cone is the classic ice cream cone shape! It also appears in rocket nose cones, decorative pillars, certain types of lampshades, and even in architecture for domed towers with conical spires.