How is the formula for the volume of a sphere derived?

drag and drop the correct word into each box to complete the explanation.

Step-by-step explanation:

From the picture we find that the sphere and the cylinder has equal heights.

i.e. cylinder has height = 2r.

x,y and r form a right triangle with hypotenuse as r.

Hence pythagorean theorem is satisfied

Area of the cross section parallel to it is area of circle with radius y

=

Volume of cylinder when 2 cones removed =

Hence volume of sphere =

The sphere and the cylinder have EQUAL heights.

A right triangle is created by the radius of the sphere r, the radius of the cross section y, and the distance between the center of the sphere and the center of the cross section x.

So  y2=r2−x2 by the Pythagorean theorem.  

2 - The area of the cross section of the sphere, and every cross section parallel to it, is .

Each cross section of the cylinder with two cones removed is the shape of an annulus with an area of  πr2−πx2 .

By Cavalieri's principle, this sphere and this cylinder with two cones removed have equal volumes.  

The volume of the cylinder with radius r and height 2r is 2πr3 .  

3 - The volume of each cone with radius r and height r is .

The volume of the cylinder with two cones removed is 43πr3 .

Therefore, the volume of the sphere is 43πr3 .

the total estimated nappy use.=10,500,000

step-by-step explanation:

given that on an average the average baby uses 3528 napkins.

in a particular year 2014, the number of births were 299697 in new south wales.

rounding off the number of births to the nearest hundred thousand we have

no of birtsh = 300000

also rounding off the average usage to nearst thousand we get

average use of a baby = 3500

hence total number of nappy estimated to be used = 3500x300000

= 10,500,000

answer is 10,500,000 nappies

i believe the answers 600m