Question

A cylinder and a cone start with the same radius and height. The radius of the cone is then tripled, and the height of the cone is cut in half. The radius of the cylinder stays the same, but the height of the cylinder is doubled. Which change produces a greater increase in volume (i.e., which figure’s volume increases by a larger factor)? Justify your answer. Write “pi” for ''pi symbol'' and “r^2”.

Answer 1

Answer:

The change in the cone produces a greater increase in volume.

Step-by-step explanation:

Let's start with the cone.

$V = \frac{1}{3} \pi r^{2} h$

$V = \frac{1}{3} \pi 3r^{2} \frac{h}{2}$         (In your case, you would type V = 1/3pi3r^2h/2)

The changes that occurred are $3^{2}$ and $1/2$. When we add these together we get $9/2$.

Now the cylinder.

$V = \pi r^{2} h$

$V = \pi r^{2} 2h$         (In your case, you would type V = pir^2 2h)

The change that occurred is $2$.

$9/2$ is greater than $2$ which means that the change in the cone produces a greater increase in volume.

Answer 2

Answer:

Step-by-step explanation:

For the cone  V k1= (Pi/3) .R squared .H

V k2= (pi/3) .  (3R)squared .  (H/2)=(9/2) .(PI/3) .  R squared.H

=(3pi/2) R.squared.H

3pi/2

nk= 2/ pi/3

N k= 9/2

For the cylinder

V c1=Pi .R squared.H

V c2= Pi.R squared.(2H)

N c=V c2/V c1=2

Cone has greatest change in volume

Hope this helps!!!!!!!!