The answers that would fill in the blanks are
- 2r
- a circle
- an annulus
- 1/3πr³
- 4/3πr³
<h3>What is the Cavalier's principle?</h3>
This principle states that if two solids are of equal altitude then the sections that the planes would make would have to be parallel and also be at the same distances from their bases which are equal such that the volumes of the solids would be equal.
Now we have to fill in the blanks with the solution.
For every corresponding pair of cross sections, the area of the cross section of a sphere with radius r is equal to the area of the cross section of a cylinder with radius r and height<u> 2r</u> minus the volume of two cones, each with a radius and height of r. A cross section of the sphere is a <u>circle</u> base of cylinder, is and a cross section of the cylinder minus the cones, taken parallel to the base of cylinder, is an <u>annulus_ </u>.The volume of the cylinder with radius r and height 2r is 2πr³, and the volume of each cone with radius r and height r is 1/3πr³. So the volume of the cylinder minus the two cones is 4/3πr³. Therefore, the volume of the sphere is by Cavalieri's principle
Read more on Cavalieri's principle here
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Answer:
1st picture: (0,4)
The lines intersect at point (0,4).
2nd picture: Graph D
2x ≥ y - 1
2x - 5y ≤ 10
Set these inequalities up in standard form.
y ≤ 2x + 1
-5y ≤ 10 - 2x → y ≥ -2 + 2/5x → y ≥ 2/5x - 2
When you divide by a negative number, you switch the inequality sign.
Now you have:
y ≤ 2x + 1
y ≥ 2/5x - 2
Looking at the graphs, you first want to find the lines that intersect the y-axis at (0, 1) and (0, -2).
In this case, it is all of them.
Next, you would look at the shaded regions.
The first inequality says the values are less than or equal to. So you look for a shaded region below a line. The second inequality says the values are greater than or equal to. So you look for a shaded region above a line.
That would mean Graph B or D.
Then you look at the specific lines. You can see that the lower line is y ≥ 2/5x - 2. You need a shaded region above this line. You can see the above line is y ≤ 2x + 1. You need a shaded region below this line. That is Graph D.
Answer: a the first answer is right
Answer:
Perimeter square = 8 sqrt(pi)
Step-by-step explanation:
The perimeter of a square is 4*s
The area of a circle is Area = pi * r^2
The circumference of a circle is C = 2*pi * r
C = 4 pi
4pi = 2*pi * r
r = 2
So the area of the circle is pi * r^2 = pi * 2^2 = 4pi
The square has the same area
Area = 4*pi
Square = 4*pi
s^2 = 4*pi
s = sqrt(4*pi)
s = 2*sqrt(pi)
The perimeter = 4 * 2 * sqrt(pi)
The perimeter = 8 * sqrt(pi)
