Combined Cone & Cone
Interactive geometry — Volume & Surface Area of a Combined Solid (Two Cones Joined at Base)
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Lower Cone Volume (V1) = ⅓πr²h1
Upper Cone Volume (V2) = ⅓πr²h2
Total Volume (V) = V1 + V2
Lower Cone CSA = πrl1 (l1 = slant height)
Upper Cone CSA = πrl2 (l2 = slant height)
Total Surface Area = πrl1 + πrl2
Slant Height (l1) = √(r² + h1²)
Slant Height (l2) = √(r² + h2²)
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 1 (Lower) — the lower cone with apex at the bottom
Cone 2 (Upper) — the upper cone with apex at the top
Slant Height (l) — distance from apex to base edge of a cone
Did You Know?
A combined solid of two cones joined at their bases forms a double cone — a shape often seen in hourglasses, spinning tops, certain crystals, and even the classic 3D diamond shape. The volume of such a solid is simply the sum of the volumes of the two cones since they share the same base radius!