Air is being pumped into a spherical balloon at the rate of cm³/min,but there is a small hole in the balloon and at the same time air is leaking out at the rate of cm³/min. Which of the following is true for ,where t is measured in minutes? A) represents the volume of the balloon after the first 10 minutes. B) represents the increase in volume each minute during the first 10 minutes. C) represents the increase in volume during the first 10 minutes.

Question

Quizplus · Accepted Answer

The rate of air being pumped in is 11 cm³/min and the rate of air leaking out is also 11 cm³/min, therefore the net rate of change of volume is 0 cm³/min. This means that the volume of the balloon is not changing at time t and so the volume of the balloon after the first 10 minutes is the same as its initial volume, which is represented by V₀.
Therefore, 11eac44f_ec98_aae1_bedf_a76cfcb52af2_TB7497_11 does not represent the volume of the balloon after the first 10 minutes.
Similarly, since the volume of the balloon is not changing, the increase in volume each minute during the first 10 minutes is also 0, and so 11eac44f_ec98_aae2_bedf_4d530eb8162c_TB7497_11 does not represent the increase in volume each minute during the first 10 minutes.
However, during the first 10 minutes, air is being pumped into the balloon at a rate of 11 cm³/min and leaking out at a rate of 11 cm³/min, resulting in a net change in volume of 0 cm³/min. Therefore, the total increase in volume during the first 10 minutes is 0, which is represented by 11eac44f_ec98_d1f3_bedf_f511917f8441_TB7497_11. This means that C is the correct answer. 
D is not a valid option.

​Air Is Being Pumped into a Spherical Balloon at the Rate

Air Is Being Pumped into a Spherical Balloon at the Rate