Combined Cylinder & Cone

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

← Back to Home

Radius: 2.0

Cyl. Height: 3.0

Cone Height: 2.0

Measurements

Total Volume:62.83 units³

Cylinder Volume:37.70 units³

Cone Volume:8.38 units³

Total Surface Area:75.40 units²

Slant Height:2.83 units

Formulas

Cylinder Volume (V_c) = πr²h_c

Cone Volume (V_k) = ⅓πr²h_k

Total Volume (V) = V_c + V_k

Cylinder CSA = 2πrh_c

Cone CSA = πrl (l = slant height)

Total Surface Area = πr² + 2πrh_c + πrl

Slant Height (l) = √(r² + h_k²)

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 two parallel circular faces

Cone — the upper part tapering to an apex

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

Did You Know?

Combined solids appear everywhere in real life — a silo (cylinder + cone roof), a pencil (hexagonal prism + cone tip), a rocket (cylinder + cone nose), and an ice cream cone (cone + hemisphere) are all combined solids!