3
QuizMultiple Choice

Composition of Functions and Modeling

Question 3 • GA-GSE Pre-Calculus

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?Use SA=4πr2.

Answer
A
7 seconds
B
10 seconds
C
49 seconds
D
196 seconds

Explanation

Use the surface area formula: 4πr² = 784π. Dividing by 4π gives r² = 196, so the fully inflated balloon has a radius of 14 cm. The radius grows at 2 cm per second, so reaching 14 cm takes 14 ÷ 2 = 7 seconds. The correct choice is 7 seconds.

AI-written and checked against the verified answer.

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