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What would be the volume of a spherical balloon after 11 seconds if the radius of the balloon is increasing at 1.3 cm/sec? Round to the nearest tenth of a centimeter. (solve by using composite functions).

Options:
Option 1: 162.8 cm^3
Option 2: 206.2 cm^3
Option 3: 216.3 cm^3
Option 4: 235.6 cm^3

1 Answer

1 vote

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.

User Dencey
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