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zhuklara [117]
1 year ago
10

Drag and drop an answer to each box to correctly complete the explanation for deriving the formula for the volume of a sphere

Mathematics
1 answer:
denis-greek [22]1 year ago
5 0

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

brainly.com/question/22431955

#SPJ1

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5x plus nine over negative six equals 3x plus 6 over negative three
Allisa [31]
Nine over negative six is three times the five gives me fifth teen and six over negative three gives me three so therefore they are not the same but 15+9=24
6 0
3 years ago
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What is the purpose of using fraction strips and a 1srip
love history [14]
the one strip is a whole fraction strip and the others are just part of the whole
8 0
3 years ago
The prism is completely filled with 1750 cubes that have edge length of 1/5 ft. What is the volume of the prism? Enter your answ
IgorC [24]

Answer:

14 ft³

Step-by-step explanation:

First, find the volume of a single cube: V = s³, where s = side length

V = s³; s = 1/5

V = (1/5)³

V = 0.008 ft³

**Note: (1/5)³ is equal to 1/125 as a fraction. I put it down in decimal form because it's easier for me to work with decimals.**

Now, to find the volume of the prism (which is <u><em>completely</em></u> filled with cubes), multiply the volume of one cube by the total number of cubes: 1750.

(1750)(0.008)

14 ft³

The volume of the prism is 14 ft³.

Hope this helps!

8 0
3 years ago
Write a rule describing the translation below
CaHeK987 [17]

Answer:

d=e

Step-by-step explanation:

3 0
3 years ago
What are the restrictions for (x^2+10x+25)/(x^2-3x-28)<br><br> 0,14<br> -4,7<br> 0,7<br> 4,7
nirvana33 [79]
The answer is -4,7

The denominator can't equal zero. Factor the denominator:
x^2 - 3x - 28=
(X - 7)(x + 4); next set each set of parentheses equal to 0;
x - 7 = 0; so x=7 is one value
x + 4 = 0; so x=-4 is the other
Remember, x = 7 and x= -4 make the denominator zero, which is a "restriction" because you can't divide by zero.
5 0
3 years ago
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