Combined Solids Explorer

Calculate Surface Area & Volume for Composite Solids

Core Concepts

Combined solids are composite shapes formed by merging two or more simple solids. Their total surface area and volume are determined by summing the contributions of each part, excluding the shared or overlapping areas.
Cylinder + Hemisphere
Volume = πr²h + (2/3)πr³
Surface Area = 2πrh + 3πr²
(Excludes shared interface)

Interactive Composite Models

V = πr²h + (2/3)πr³
SA = 2πrh + 3πr²
Volume: 0 cm³
Surface Area: 0 cm²
V = πr²(cylH) + (1/3)πr²(coneH)
SA = 2πr(cylH) + πr·√(r²+coneH²) + πr²
Volume: 0 cm³
Surface Area: 0 cm²

Volume Comparison Tool

1 Unit Cube = 1 cm³
Composite contains ≈ 0 unit cubes

Practice Challenges

A composite solid consists of a cylinder with a hemisphere on top. The cylinder has a radius of 5 cm and a height of 10 cm. Calculate its total volume and surface area.

Volume = π×5²×10 + (2/3)π×5³ = 250π + (250/3)π ≈ 1047.2 cm³
Surface Area = 2π×5×10 + 3π×5² = 100π + 75π = 175π ≈ 549.8 cm²

A composite solid consists of a cylinder with a hemisphere on top. The cylinder has a radius of 4 cm and a height of 8 cm. Calculate its total volume and surface area.

Volume = π×4²×8 + (2/3)π×4³ = 128π + (128/3)π ≈ 536.2 cm³
Surface Area = 2π×4×8 + 3π×4² = 64π + 48π = 112π ≈ 351.9 cm²

A composite solid has a total volume of 1500 cm³ and consists of a cylinder with a hemisphere on top. If the cylinder's height is twice the radius, find the radius.

Let r be the radius and h = 2r. Then, volume = 2πr³ + (2/3)πr³ = (8/3)πr³.
Solving: r³ = (1500×3)/(8π) ≈ 179.0, hence r ≈ 5.65 cm.

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