Question

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 _________.

Answer 1

√2 or 1.414

Step-by-step 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* A_1\\\Rightarrow 4\pi r_2^2=2* 4\pi r_1^2\\\Rightarrow r_2^2=2r_1^2\\\Rightarrow r_2=√(2)r_1=1.414r_1`

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