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Question

A soap bubble will enclose the maximum space with a minimum amount of surface material. Architects have used this principle to create buildings that enclose a great amount of space with a small amount of building material. If a soap bubble has a surface area of A, then its volume V is given by the equation $V=0.094 \sqrt{A^{3}}$. Find the surface area of a bubble with a volume of $1.75 \times 10^{2}$ cubic millimetres.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 3$V=0.094\sqrt{A^3}$ $V=0.094A^{\frac{3}{2}}$ $V^{\frac{2}{3}}=(0.094A^{\frac{3}{2}})^{\frac{2}{3}}$ $V^{\frac{2}{3}}=(0.094)^{\frac{2}{3}}A$

$\dfrac{V^{\frac{2}{3}}}{(0.094)^{\frac{2}{3}}}=A$

determine an expression for the surface area

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