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murzikaleks [220]
3 years ago
13

A spherical balloon is partially blown up and its surface area is measured. More air is then added, increasing the volume of the

balloon. If the surface area of the balloon expands by a factor of 2.00 during this procedure, by what factor does the radius of the balloon increase? The radius of the balloon increases by a factor of _________.
Physics
1 answer:
Aloiza [94]3 years ago
5 0

Answer:

√2 or 1.414

Explanation:

Area of a sphere

A=4\pi r^2

Initial area of the balloon

A_1=4\pi r_1^2

Final area of the balloon

A_2=4\pi r_2^2

Given that

A_2=2\times A_1\\\Rightarrow 4\pi r_2^2=2\times 4\pi r_1^2\\\Rightarrow r_2^2=2r_1^2\\\Rightarrow r_2=\sqrt{2}r_1=1.414r_1

Hence, the radius increases by a factor of √2 or 1.414

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