To find the work done to make a soap bubble bigger, we use the formula: W=2T⋅∆A Step 1: Find Change in Surface Area for W1 The surface area of a sphere is 4πr2. When the radius goes from r to 2r, the change in area is: ∆A=4π(2r)2−4πr2 This simplifies to: =16πr2−4πr2=12πr2 Step 2: Find Work Done W1 Plug the change in area into the work formula: W1=2T⋅12πr2=24πTr2 Step 3: Find Change in Surface Area for W2 Now, change the radius from 2r to 3r : ‌∆A=4π(3r)2−4π(2r)2 ‌=36πr2−16πr2=20πr2 Step 4: Find Work Done W2 Plug in this change in area: W2=2T⋅20πr2=40πTr2 Step 5: Ratio W1:W2 W1:W2=24:40=3:5
