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Sagot :
Answer:
The volume of the sphere is increasing at a rate of 56,549 cubic millimeters per second.
Step-by-step explanation:
Volume of a sphere:
The volume of a sphere is given by:
[tex]V = \frac{4\pi r^3}{3}[/tex]
In which r is the radius.
Solving this question:
The first step do solve this question is derivating V implictly in function of t. So
[tex]\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}[/tex]
The radius of a sphere is increasing at a rate of 5 mm/s.
This means that [tex]\frac{dr}{dt} = 5[/tex]
Diameter is 60 mm
This means that [tex]r = \frac{60}{2} = 30[/tex]
How fast is the volume increasing (in mm3/s) when the diameter is 60 mm?
This is [tex]\frac{dV}{dt}[/tex]. So
[tex]\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}[/tex]
[tex]\frac{dV}{dt} = 4\pi*30^2*5 = 900*20\pi = 56549[/tex]
The volume of the sphere is increasing at a rate of 56,549 cubic millimeters per second.
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