Question

The radius of a sphere-shaped balloon increases at a rate of 2 centimeters (cm) per second. If the surface area of the completely inflated balloon is 784π cm2, how long will it take for the balloon to fully inflate?

Answer 1

Considering the surface area of the spherical ballon, it will take 7 seconds for the the balloon to fully inflate.

What is the surface area of a sphere?

The surface area of a sphere of radius r is given by:

$S = 4\pi r^2$

In this problem, the surface area is of $784\pi$ cm², hence the radius in cm is found as follows:

$784\pi = 4\pi r^2$

$4r^2 = 784$

$r^2 = \frac{784}{4}$

$r^2 = 196$

$r = \sqrt{196}$

r = 14 cm.

The radius start at 0 cm, inflating at a rate of 2 cm/s, hence it will take 7 seconds for the the balloon to fully inflate, as 14 cm/(2 cm/s) = 7 s.

More can be learned about the surface area of a sphere at https://brainly.com/question/21207980

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