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:
brainly.com/question/25814490
Answer:
m<BAC = 34
Step-by-step explanation:
It is given that (<BOC) is a central angle with a degree measure of (68). A central angle is an angle whose vertex is the center of the circle. (<BAC) is an inscribed angle, an angle whose vertex is on the circumference (perimeter) of the circle. Arc (BC) connects the ends of both of these angles.
The central angle theorem states that the measure of the central angle is equivalent to its surrounding arc. Using this theorem, one can state the following,
m<BOC = BC = 68
The inscribe angle theorem states that the measure of the arc surrounding the inscribed angle is twice the measure of the inscribed angle. Applying this theorem, one can state the following,
2(m<BAC) = (BC)
2 (m<BAC) = 68
m<BAC = 34
x + 2