How fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
To solve the question, we need to know the volume of a sphere
<h3>
Volume of a sphere</h3>
The volume of a sphere V = 4πr³/3 where r = radius of sphere.
<h3>How fast the volume of the sphere is changing</h3>
To find the how fast the volume of the sphere is changing, we find rate of change of volume of the sphere. Thus, we differentiate its volume with respect to time.
So, dV/dt = d(4πr³/3)/dt
= d(4πr³/3)/dr × dr/dt
= 4πr²dr/dt where
- dr/dt = rate of change of radius of sphere and
- 4πr² = surface area of sphere
Given that
- dr/dt = + 3 cm/s (positive since it is increasing) and
- 4πr² = surface area of sphere = 10 cm²,
Substituting the values of the variables into the equation, we have
dV/dt = 4πr²dr/dt
dV/dt = 10 cm² × 3 cm/s
dV/dt = 30 cm³/s
So, how fast the volume of the sphere is changing when the surface area is 10 square centimeters is it is increasing at a rate of 30 cm³/s.
Learn more about how fast volume of sphere is changing here:
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x^2 + 3x + 9
i hope that's what your looking for
1.085 litres is the juice left at the end of the day
Answer:
3 ≤ n < 15
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1-2. not n
3-4. yes n
5-6. yes n
7-8. yes n
9-10. yes n
11-12. yes n
13-14. yes n
15-16. not n
Step-by-step explanation:
Everything on this side is less than, < but everything on this side is greater.
Everything on this side could be equal or less, ≤ but everything on this side is
not.
I'm had a hard time with the number line, but imagine a line going through the periods and there being a dot where the yes ns end, and start.
Intervals has each point represent more than one number making the line shorter.
