Final answer:
The volume of the spherical balloon after 11 seconds is approximately 235.6 cm³. Option 4 is correct.
Step-by-step explanation:
To find the volume of the balloon after 11 seconds, we first need to find the radius of the balloon after 11 seconds. The radius of the balloon is increasing at a rate of 1.3 cm/sec, so after 11 seconds, the radius will be:
= 1.3 cm/sec × 11 sec
= 14.3 cm
[I have highlighted the key steps to solve the problem using composite functions. Feel free to use different words or notations as you like]
Next, we can use the formula for the volume of a sphere to find the volume of the balloon. The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume and r is the radius.
Plugging in r = 14.3 cm, we get:
V = (4/3)π(14.3 cm)³
V≈ 235.6 cm³.
Therefore, the volume of the spherical balloon after 11 seconds is approximately 235.6 cm³.
So the answer is Option 4.