Answer:
Step-by-step explanation:
Area of plane figures
Being r the radius of a circle, the area of a sector defined by an angle is
If a is the repeated side of an isosceles triangle and is the angle they define, then the area of the triangle is
The figure shows a circle with radius of r=7 cm. The white area is equal to the area of the circle minus the blue area
The area of the circle is
The blue area is the sum of the sector defined by the angle (360-150)= and the triangle. An angle of is equivalent to
The area of the sector is
The area of the triangle with center angle 150^o is
The blue area is
Finally, the white area is
Sorry i cant answer youtr question, can you make it more detailed?
Split up the integration interval into 4 subintervals:
The left and right endpoints of the -th subinterval, respectively, are
for , and the respective midpoints are
We approximate the (signed) area under the curve over each subinterval by
so that
We approximate the area for each subinterval by
so that
We first interpolate the integrand over each subinterval by a quadratic polynomial , where
so that
It so happens that the integral of reduces nicely to the form you're probably more familiar with,
Then the integral is approximately
Compare these to the actual value of the integral, 3. I've included plots of the approximations below.
The volume of the hemisphere will always be greater. Here is an example:
Volume of the sphere when the radius is 2
Volume of the hemisphere when the radius is 6
The answer is 0.00125139043