Final answer:
After 5 minutes, the volume of the melting ice cream is 270 cm³, and the rate of decrease in volume is -8 cm³/min. Thus the correct option is (D).
Step-by-step explanation:
At first, let's assume that we have a spherical scoop of ice cream with an initial volume of 300 cm³. The rate at which this ice cream is melting is given as 3 cm³/min. This means that every minute, we lose a volume of ice cream equal to 3 cm³. After a certain time, the remaining volume will be less than the initial volume. In this case, we want to find out how much ice cream is left after five minutes. Thus the correct option is (D).
To calculate the final volume, we need to subtract the amount that has melted during those five minutes from the initial volume. The amount that has melted during those five minutes is equal to five times the rate at which it is melting (since we are losing three cubic centimeters every minute). Therefore, the final volume will be:
Final Volume = Initial Volume - (Rate of Decrease) x Time Taken (in Minutes)
Final Volume = 300 cm³ - (3 cm³/min) x 5 min
Final Volume = 270 cm³
Now that we have found out the final volume, we can calculate the rate at which the ice cream is melting after five minutes. The rate at which it is melting now is equal to the difference between the final and initial volumes divided by the time taken. Therefore, our answer would be:
Rate of Decrease After Five Minutes = (Final Volume - Initial Volume) / Time Taken (in Minutes)
Rate of Decrease After Five Minutes = (270 cm³ - 300 cm³) / 5 min
Rate of Decrease After Five Minutes = -8 cm³/min