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Model: For coalescing soap bubbles at the same level, \\[ R^3 \\approx r_1^3 + r_2^3. \\]
Substitute values: \\[ R^3 = ${a}^3 + ${b}^3 = ${ (a**3).toFixed(3) } + ${ (b**3).toFixed(3) } = ${(a**3 + b**3).toFixed(3)}. \\]
Take cube root: \\[ R = \\sqrt[3]{${(a**3 + b**3).toFixed(3)}} \\approx ${R.toFixed(decimals)}~\\text{cm}. \\]

Q6. Coalescing Soap Bubbles — Interactive Worksheet

Problem. Two soap bubbles of radii \(r_1\) and \(r_2\) coalesce. Ignoring pressure change with height and assuming isothermal conditions, find the radius \(R\) of the resulting bubble.

Use the coalescing relation \(R^3 \approx r_1^3+r_2^3\).

Given \(r_1\) (cm)

Given \(r_2\) (cm)

Decimal places for \(R\)

Your computed answer \(R\) (cm)

Steps (auto-filled from your inputs)

Solution Enter values and click “Show steps & solution”.