Answer :
The rate of change of the volume of sphere when is decreasing at a constant rate is found as 3319.16 cm³/min.
Define the term rate of change?
- An indicator of how some quantity changes in proportion to another is called a rate of change.
- If x and y are the independent and dependent variables, respectively, then rate of change is equal to y-to-x conversions.
- Positive or negative change rates are possible.
For the stated question-
- A sphere's radius is shrinking at a steady rate of 5 centimeters per minute.
- The sphere's volume is 1611 cubic centimeters at that precise moment,
Thus, the volume of sphere is found by the equation.
Volume of sphere V = 4/3 πr³
V = 1611 cm³.
1611 = 4/3 πr³
On solving,
r = 7.27 cm
Rate change of the volume;
dV/dt = 4/3 πr² × 3
dV/dt = 4 πr²
Put r = 7.27 cm and π = 3.14
dV/dt = 4 x 3.14 x 7.27²
dV/dt = 3319.16 cm³/min.
Thus, the rate of change of the volume of sphere when is decreasing at a constant rate is found as 3319.16 cm³/min.
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