What is the relationship between a cylinder and a sphere with the same base area and perpendicular height?

For a sphere, the height is equal to the diameter, or two times the radius.

and because both objects have the same base area, then we can take the radius of the sphere equal to R and the radius of the base of the cylinder also equal to R.

The volume of the cylinder is:

Vc = pi*r^2*h

and here we have r = R and h = 2R

V = pi*(R^3)*2

the volume of a sphere of radius R is:

Vs = (4/3)*pi*R^3

The quotient between them is:

Vc/Vs = 2/(4/3) = 6/4 = 3/2.

This means that the volume of the cylinder is 3/2 times the volume of the sphere, always, for any value of R.

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

step-by-step explanation: